Back to the home page of A. Grigor'yan

Publications of Alexander Grigor'yan

Profile from MathSciNet
List from MathSciNet

Profile from zbMATH
List from zbMATH

  1. Grigor'yan, A., Lin Yong, Muranov, Yu., Yau S.-T., Path chain complex and path homology on a digraph, to appear in Proceedings of ICBS (pdf) 
  2. Grigor'yan, A., Hu Eryan, Hu Jiaxin, Tail estimates and off-diagonal upper bounds of the heat kernel, preprint, 2024 (pdf)
  3. Grigor'yan, A., Pessoa, L.F., Setti, A.G., Lp-parabolicity of Riemannian manifolds, preprint, 2024 (pdf)
  4. Grigor'yan, A., Lin Yong, Yau, S.-T., Zhang Haohang, Eigenvalues of the Hodge Laplacian on digraphs, to appear in Comm. Anal. Geom. (pdf)
  5. Grigor'yan, A., Sürig, P., Upper bounds for solutions of Leibenson’s equation on Riemannian manifolds, preprint, 2024 (pdf)
  6. Grigor'yan, A., Sürig, P., Sharp propagation rate for solutions of Leibenson's equation on Riemannian manifolds, to appear in Ann. Scuola Norm. Sup. Pisa (pdf)
  7. Grigor'yan, A., Hu Eryan, Hu Jiaxin, Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces, Math. Annalen 389 (2024) no.3, 2411-2467  DOI:10.1007/s00208-023-02699-3  (pdf)
  8. Grigor'yan, A., Sürig, P., Finite propagation speed for Leibenson's equation on Riemannian manifolds, Comm. Anal. Geom. 32 (2024) no.9, 2467-2504 (pdf)
  9. Grigor'yan, A., Hu Eryan, Hu Jiaxin, Mean value inequality and generalized capacity on doubling spaces, Pure and Applied Funct. Anal. (2024), "Maz'ya Birthday Volume", 111-168 (pdf)
  10. Grigor'yan, A., Lin Yong., Yau S.-T., Analytic and Reidemeister torsions of digraphs and path complexes, Pure Appl. Math. Quaterly 20 (2024) no.2, 703-755 (pdf)
  11. Grigor'yan, A., Analysis on ultra-metric spaces via heat kernels, p-Adic Numbers, Ultrametric Analysis and Applications  15 (2023) no.3, 204-242, "Vladimirov-100 Volume" (pdf)
  12. Grigor'yan, A., Hu Eryan, Hu Jiaxin, Off-diagonal lower estimates and Hölder regularity of the heat kernel, Asian J. Math., 27 (2023) no.5,  "K.-S.Lau Memorial Volume" , 675-770. (pdf)
  13. Bendikov, A., Grigor'yan, A., Molchanov, S., Hierarchical Schrödinger operators with singular potentials, Proc. Steklov Institute of Mathemathics 323 (2023)  "Besov Birthday Volume", 12-46  (pdf)
  14. Grigor'yan, A., Lectures on path homology theory of digraphs, monograph,  TOC, Preface, Bibliography
  15. Grigor'yan, A., Papageorgiou, E., Zhang Hong-Wei, Asymptotic behaviour of the heat semigroup on certain Riemannian manifolds, in: "From Classical Analysis to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 1", Applied and Numerical Harmonic Analysis, Birkhäuser, 2023. 165-179. DOI:10.1007/978-3-031-37800-3  (pdf)
  16. Grigor'yan, A., Ishiwata, S., Saloff-Coste, L., Poincaré constant on manifolds with ends,  Proc. LMS  126 (2023) no.6, 1961-2012.  DOI:10.1112/plms.12522 (pdf)
  17. Grigor'yan, A., Muranov, Yu., On homology theories of cubical digraphs, Pacific J. Math., 322 (2023) no.1, 39-58 (pdf)
  18. Grigor'yan, A., Advances in path homology theory of digraphs, Notices of the ICCM, 10 (2022) no.2, 61-124 (pdf)
  19. Grigor'yan, A., Lin Yong., Yau S.-T., Discrete tori and trigonometric sums,  J. Geom. Anal. 32 (2022) art. 298 "Peter Li Birthday Volume"  (pdf)
  20. Grigor'yan, A., Sürig, P., Volume growth and on-diagonal heat kernel bounds on Riemannian manifolds with an end, Potential Analysis (2022),  DOI:10.1007/s11118-022-10044-7 (pdf)
  21. Grigor'yan, A., Analysis on fractal spaces and heat kernels, in: "Dirichlet Forms and Related Topics", Springer Proceedings in Mathematics & Statistics 394 (2022), "Fukushima Birthday Volume", 143-159 (pdf)
  22. Cao Jun, Grigor'yan, A.,  Heat kernels and Besov spaces on metric measure spaces, J. d'Analyse Mathématique  148 (2022) 637-680.  DOI: 10.1007/s11854-022-0239-y  (pdf)
  23. ed. Grigor'yan, A., Sun Yuhua, "Analysis and partial differential equations on manifolds, fractals and graphs", de Gruyter series Advances in Analysis and Geometry 3, 2021. 
  24. Grigor'yan, A., Analysis on manifolds and volume growth, Advances in Analysis and Geometry 3 (2021) 299-324 (pdf)
  25. Grigor'yan, A., Ishiwata, S., Saloff-Coste, L., Geometric analysis on manifolds with ends, Advances in Analysis and Geometry 3 (2021) 325-344 (pdf)
  26. Grigor'yan, A., Hu Eryan, Hu Jiaxin, The pointwise existence and properties of heat kernel, Advances in Analysis and Geometry 3 (2021) 27-70 (pdf)
  27. Bendikov, A., Grigor'yan, A., Molchanov, S., Hierarchical Schrödinger type operators: the case of locally bounded potentials, Operator Theory and Harmonic Analysis 358 (2021) 43-90 (pdf)
  28. Cao Jun, Grigor'yan, A., Liu Liguang, Hardy's inequality and Green function on metric measure spaces,  J. Funct. Anal., 281 (2021) art. 109020 (pdf)
  29. Grigor'yan, A., Jimenez, R., Muranov, Yu., Homology of digraphs, Math. Notes., 109 (2021), no.5, 712-726  (pdf) Russian original: Matem. Zam. 109 (2021) no.5, 705-722.
  30. Bendikov, A., Grigor'yan, A., Hu Eryan, Hu Jiaxin, Heat kernels and non-local Dirichlet forms on ultra-metric spaces, Ann. Scuola Norm. Sup. Pisa, XXII (2021) 399-461 (pdf)
  31. Grigor'yan, A., Mathematical riddles of COVID-19, unpublished manuscript, 2020 (pdf)
  32. Grigor'yan, A., Sun Yuhua, Verbitsky, I., Superlinear elliptic inequalities on manifolds, J. Funct. Anal., 278 (2020) art. 108444. DOI:10.1016/j.jfa.2019.108444 (pdf) 
  33. Grigor'yan, A., Verbitsky, I., Pointwise estimates of solutions to nonlinear equations for nonlocal operators, Ann. Scuola Norm. Sup. Pisa, XX (2020) 721-750  (pdf)
  34. Cao Jun, Grigor'yan, A.,  Heat kernels and Besov spaces associated with second order divergence form elliptic operators, J. Fourier Analysis Appl., 26 (2020) art. 3. DOI:10.1007/s00041-019-09708-7 (pdf)
  35. Faraji, S., Grigor'yan, A., On biparabolicity of Riemannian manifolds,  Rev. Mat. Iberoam. 35 (2019) 2025-2034 (pdf)
  36. Grigor'yan, A., Sun Yuhua,  On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds, Calc. Var. PDEs  58 (2019) art. 207. DOI: 10.1007/s00526-019-1645-6 (pdf) 
  37. Grigor'yan, A., Jimenez, R., Muranov, Yu., Yau, S.-T., Homology of path complexes and hypergraphs, Topology Appl., 267 (2019) art. 106877. DOI: 10.1016/j.topol.2019.106877 (pdf)
  38. Grigor'yan, A., Yang Meng, Local and non-local Dirichlet forms on the Sierpinski carpet, Trans. AMS, 372 (2019) 3985-4030 (pdf)
  39. Grigor'yan, A., Analysis and stochastic processes on metric measure spaces, in: "Spectral Structures and Topological Methods in Mathematics", ed. M. Baake, F.Götze, W. Hoffmann, EMS, 2019. 55-73 (pdf)
  40. Grigor'yan, A., Verbitsky, I., Pointwise estimates of solutions to semilinear elliptic equations and inequalities, J. d'Analyse Mathématique 131 (2019) no.2,  559-601. DOI:10.1007/s11854-019-0004-z  (pdf)
  41. Grigor'yan, A., Yau in my life, ICCM Notices, 7 (2019) 43-45. "S.-T. Yau  Birthday Volume ". 
  42. Grigor'yan, A., Introduction to Analysis on Graphs, a textbook, AMS University Lecture Series 71, 2018, 168 pp. AMS bookstore, TOC and Preface, Bibliography and Index, Solutions to exercises 
  43. Grigor'yan, A., Muranov, Yu., Vershinin, V., Yau S.-T., Path homology theory of multigraphs and quivers, Forum Math 30 (2018) 1319-1337. DOI: 10.1515/forum-2018-0015 (pdf)
  44. Grigor'yan, A., Kondratiev, Yu., Piatnitski, A., Zhizhina, E., Pointwise estimates for heat kernels of convolution- type operators, Proc. LMS, 117 (2018) no.4, 849-880. DOI: 10.1112/PLMS.12144  (pdf)
  45. Grigor'yan, A., Hu Eryan, Hu Jiaxin, Two-sided estimates of heat kernels of jump type Dirichlet forms, Advances in Math., 330 (2018) 433-515 (pdf)
  46. Grigor'yan, A., Yang Meng, Determination of walk dimension of Sierpinski gasket without using diffusion,  J. Fract. Geom. 5 (2018) 419-460 (pdf)   
  47. Grigor'yan, A., Ishiwata, S., Saloff-Coste, L., Heat kernel estimates on connected sums of parabolic manifolds,  J. Math. Pures Appl. 113 (2018) 155-194 (pdf, appendix)
  48. Grigor'yan, A., Jimenez, R., Muranov, Yu., Yau, S.-T., On the path homology theory of digraphs and Eilenberg-Steenrod axioms, Homology, Homotopy and Applications 20 (2018), 179-205 (pdf)
  49. Grigor'yan, A., Ouyang, S.-X., Roeckner, M., Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities,  J. Reine Angew. Math. 736 (2018) 1-31. DOI: 10.1515/crelle-2015-0026 (pdf). 
  50. Grigor'yan, A., Jimenez, R., Muranov, Yu., Fundamental groupoids of digraphs and graphs, Czech Math. J., 68 (2018) 35-65 (pdf)
  51. Grigor'yan, A., Hu Eryan, Hu Jiaxin, Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces,  J. Funct. Anal. 272 (2017) 3311-3346 (pdf)
  52. Grigor'yan, A., Muranov, Yu., Yau S.-T.,  Homologies of digraphs and Künneth formulas,  Comm. Anal. Geom, 25 (2017) 969-1018 (pdf)
  53. Grigor'yan, A., Lin Yong, Yang Yunyan,  Existence of positive solutions to some nonlinear equations on locally finite graphs, Science China Math. 60 (2017) 1311-1324 (pdf)
  54. Grigor'yan, A., Losev, A., Dimension of spaces of solutions of Schrödinger equation on noncompact Riemannian manifolds, Math. Physics and Computer Simulations, 20 (2017) 34-42.
  55. Grigor'yan, A., Kajino, N., Localized upper bounds of heat kernel for diffusions via a multiple Dynkin-Hunt formula, Trans. AMS, 369 (2017) 1025-1060  (pdf) 
  56. Grigor'yan, A., Lin Yong, Muranov, Yu., Yau S.-T., Path complexes and their homologies,  J. Math. Sciences, 248 (2020) no.5, 564-599 (pdf)  Russian original: Fundam. i prikl. matem. 21 (2016) no.5, 79-128 (pdf)
  57. Grigor'yan, A., Lin Yong, Yang Yunyan,  Kazdan-Warner equations on graphs, Calc. Var. PDEs, 55 (2016) paper no. 92 (pdf)
  58. Grigor'yan, A., Lin Yong, Yang Yunyan,  Yamabe type equations on finite graphs, J. Diff. Eq., 261 (2016) 4924-4943 (pdf)
  59. Grigor'yan, A., Saloff-Coste, L., Surgery of the Faber-Krahn inequality and applications to heat kernel bounds, J. Nonlinear Analysis, 131 (2016) 243-272 (pdf)
  60. Grigor'yan, A., Nadirashvili, N., Sire, Y., A lower bound for the number of negative eigenvalues of Schrödinger operators, J. Diff. Geom., 102 (2016)  395-408  (pdf)
  61. Grigor'yan, A., Muranov, Yu., Yau S.-T., On a cohomology theory of digraphs and Hochschild cohomology, J. Homotopy Relat. Struct. 11 (2016) 209-230 (pdf)
  62. Grigor'yan, A., Hu Jiaxin., Lau, K.-S., Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric spaces, J. Math. Soc. Japan, 67 (2015) 1485-1549 (pdf)
  63. Bendikov, A., Grigor'yan, A., Molchanov, S., Samorodnitsky, G., On a class of random perturbations of the hierarchical Laplacian, Izv. Math. 79 (2015) 859-894 (pdf) Russian original: Izvestiya RAN, Ser. Mat. 79 (2015) no.5, 3–38.
  64. Grigor'yan, A., Nadirashvili, N., Negative eigenvalues of two-dimensional Schrödinger operators, Archive Rat. Mech. Anal., 217 (2015) no.3, 975-1028  (pdf) Correction
  65. Grigor'yan, A., Lin Yong, Muranov, Yu., Yau S.-T.,  Cohomology of digraphs and (undirected) graphs,  Asian J. Math., 19 (2015) 887-932 (pdf)
  66. Grigor'yan, A., Liu Liguang, Heat kernel and Lipschitz-Besov spaces,  Forum Math., 27 (2015) 3567-3613  (pdf)
  67. Grigor'yan, A., Hu Jiaxin, Lau, K.-S. Estimates of heat kernels for non-local regular Dirichlet forms, Trans. AMS,  366 (2014), 6397-6441 (pdf)
  68. Grigor'yan, A., Lin Yong, Muranov, Yu., Yau S.-T., Homotopy theory of digraphs,  Pure Appl. Math Quaterly 10 (2014) no.4 619-674 (pdf)
  69. Grigor'yan, A., Muranov, Yu., Yau S.-T., Graphs associated with simplicial complexes,  Homology, Homotopy and Applications 16 (2014) 295-311 (pdf)
  70. Grigor'yan, A., Hu Jiaxin, Lau, K.-S., Heat kernels on metric measure spaces, in "Geometry and Analysis on Fractals", Springer Proceedings in Mathematics & Statistics, 88 (2014)147-208  (pdf)
  71. Grigor'yan, A., Huang, X.-P., Stochastic completeness of jump processes on metric measure spaces, in "Geometry and Analysis on Fractals", Springer Proceedings in Mathematics & Statistics, 88 (2014) 209-224 (pdf)
  72. Bendikov, A., Grigor'yan, A., Pittet, Ch., Woess, W., Isotropic Markov semigroups on ultra-metric spaces, Russian Math Surveys 69 (2014) no.4,  589-680  (pdf). Russian version: UMN 69 (2014) 3-102 (pdf) 
  73. Grigor'yan, A., Sun Yuhua.  On non-negative solutions of the inequality ∆u+uσ≤0 on Riemannian manifolds, Comm. Pure Appl. Math., 67 (2014) no.8, 1336-1352 (pdf)
  74. Grigor'yan, A., Hu Jiaxin, Heat kernels and Green functions on metric measure spaces, Canad. J. Math. 66 (2014) no.3, 641-699 (pdf)
  75. Grigor'yan, A., Hu Jiaxin, Upper bounds of heat kernels on doubling spaces, Moscow Math. J. 14 (2014) 505-563 (pdf, ps) 
  76. Grigor'yan, A., Lin Yong, Muranov, Yu., Yau S.-T., Homologies of path complexes and digraphs, arXiv:1207.2834v4 (2013), 88 pages (pdf)
  77. Grigor'yan, A., Stochastic completeness of symmetric Markov processes and volume growth,  Rend. Sem. Mat. Univ. Pol. Torino 71 (2013) no.2, 227-237 (pdf)
  78. Grigor'yan, A., Masamune, J., Parabolicity and stochastic completeness of manifolds in terms of the Green formula, J. de Mathématiques Pures et Appliquées 100 (2013) no.5 607-632 (pdf)
  79. Grigor'yan, A., Ishiwata, S., Heat kernel estimates on a connected sum of two copies of Rn along a surface of revolution,  Global and Stochastic Analysis 2 (2012) no.1  29-65 (pdf)
  80. Bendikov, A., Grigor'yan, A., Pittet, Ch., On a class of Markov semigroups on discrete ultra-metric spaces, Potential Analysis 37 (2012) no. 2 125-169 (pdf)
  81. Grigor'yan, A., Huang X.-P., Masamune, J.,  On stochastic completeness of jump processes, Math. Z. 271 (2012) no. 3 1211-1239 (pdf)
  82. Van den Berg, M., Gilkey, P., Grigor'yan, A., Kirsten, K., Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data, Comm. PDEs 37 (2012) 885-900. (pdf)
  83. Grigor'yan, A., Telcs, A., Two-sided estimates of heat kernels on metric measure spaces, Annals of Probability 40 (2012) 1212-1284 (pdf)
  84. Barlow, M.T., Grigor'yan, A., Kumagai, T., On the equivalence of parabolic Harnack inequalities and heat kernel estimates, J. Math. Soc. Japan 64 (2012) no.4 1091-1146 (pdf)
  85. Grigor'yan, A., Hu Jiaxin, Lau K.-S. Comparison inequalities for heat semigroups and heat kernels on metric measure spaces,  J. Funct. Anal. 259 (2010) 2613–2641 (pdf)
  86. Grigor'yan, A., Kondratiev, V.A., On the existence of positive solutions of semi-linear elliptic inequalities on Riemannian manifolds,  in "Around the Research of Vladimir Maz'ya II, Partial Differential Equations", ed. A.Laptev, International Mathematical Series 12, Springer, 2010. 203-218. (pdf, ps)
  87. Grigor'yan, A., Heat kernels on metric measure spaces with regular volume growth, in "Handbook of Geometric Analysis (Vol. II)" ed. L. Ji, P. Li, R. Schoen, L. Simon, Advanced Lectures in Math. 13, International Press, 2010. 1-60. (pdf, ps)
  88. Grigor'yan, A., Yau's work on heat kernels,  in "Geometry and Analysis (Vol. I)",  Advanced Lectures in Math. 17, International Press, 2010. 113-117.
  89. Grigor'yan, A., Heat Kernel and Analysis on Manifolds, a monograph, AMS/IP Studies in Advanced Mathematics, 47, 2009. Exercises, Solutions,  AMS Bookstore, TOC and Preface, Bibliography and Index,  AMS site of the book
  90. Grigor'yan, A., Hu Jiaxin, Lau K.-S.,  Heat kernels on metric spaces with doubling measure, in "Fractal Geometry and Stochastics IV", Progress in Probability 61, Birkhäuser, 2009. 3-44. (pdf)
  91. Grigor'yan, A., Hsu, Elton P., Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold,  in "Sobolev Spaces in Mathematics II" ed. V. Maz'ya, "Sergey Sobolev Centenary Volume", International Mathematical Series, Springer, 2009. 209-225. (pdf, ps)
  92. Grigor'yan, A., Saloff-Coste, L. Heat kernel on manifolds with ends, Ann. Inst. Fourier, Grenoble, 59 (2009) no.5, 1917-1997 (pdf, ps)
  93. Barlow, M.T.,  Grigor'yan, A., Kumagai, T., Heat kernel upper bounds for jump processes and the first exit time, J. Reine Angew. Math.,  626 (2009) 135-157 (pdf, ps) 
  94. Grigor'yan, A.  Heat kernel upper bounds on fractal spaces, unpublished manuscript, 2004. (pdf, ps). The results of this manuscript are covered by those of the paper Grigor'yan, A., Hu J., Upper bounds of heat kernels on doubling spaces, Moscow Math. J. 14 (2014) 505-563.
  95. Grigor'yan, A., Kumagai, T. On the dichotomy in the heat kernel two sided estimates,  Proceedings of Symposia in Pure Mathematics 77 (2008)  199-210 (pdf, ps)
  96. Grigor'yan, A., Hu, Jiaxin, Off-diagonal upper estimates for the heat kernel of Dirichlet forms on metric spaces,  Invent. Math.  174 (2008)  81-126. (pdf, ps)
  97. Grigor'yan, A., Hansen, W. Lower estimates for a perturbed Green function,  Journal d'Analyse Mathematique, 104 (2008) 25-58. (pdf, ps)
  98. Grigor'yan, A., Hu Jiaxin, Lau K.-S. Obtaining upper bounds of heat kernels from lower bounds,   Comm. Pure Appl. Math.  61 (2008) 639-660. (pdf, ps)
  99. Grigor'yan, A., Hu Jiaxin, Lau K.-S. Equivalence conditions for on-diagonal upper bounds of heat kernels on self-similar spaces,  J. Funct. Anal. 237 (2006) 427-445. (pdf, ps)
  100. Grigor'yan, A.  Heat kernels on weighted manifolds and applications,  Cont. Math. 398 (2006) 93-191. (pdf, ps) 
  101. Coulhon T., Grigor'yan A., Zucca F. The discrete integral maximum principle and its applications, Tohoku J. Math. 57 (2005) no.4, 559-587. (pdf, ps)
  102. Grigor'yan, A., Saloff-Coste, L., Stability results for Harnack inequalities, Ann. Inst. Fourier, Grenoble 55 (2005) no.3, 825-890. (pdf)
  103. Grigor'yan A., Netrusov Yu., Yau S.-T. Eigenvalues of elliptic operators and geometric applications, Surveys in Differential Geometry, IX (2004) 147-218.  (pdf, ps)
  104. ed. Grigor'yan A., Yau S.-T. “Eigenvalues of Laplacians and other geometric operators”,  Surveys in Differential Geometry, IX. International Press, 2004.
  105. Grigor'yan, A. Heat kernels and function theory on metric measure spaces, Cont. Math. 338 (2003) 143-172 (pdf, ps)
  106. ed.  Auscher P., Coulhon T., Grigor'yan A.  “Heat kernels, random walks, and analysis on manifolds and graphs”, Contemporary Mathematics, 338, AMS, 2003.
  107. Grigor'yan, A., Yau, S.-T. Isoperimetric properties of higher eigenvalues of elliptic operators,  Amer. J. Math. 125 (2003) 893-940 (pdf, ps)
  108. Coulhon, T., Grigor'yan, A., Levin, D. On isoperimetric profiles of product spaces, Comm. Anal. Geom. 11 (2003) no.1, 85-120. (pdf, ps, dvi)
  109. Grigor'yan, A., Hu Jiaxin, Lau K.-S. Heat kernels on metric-measure spaces and an application to semi-linear elliptic equations, Trans. AMS 355 (2003) no.5, 2065-2095. (pdf, ps)
  110. Grigor'yan, A., Kelbert, M. Recurrence and transience of branching diffusion processes on Riemannian manifolds, Annals of Probability 31 (2003) no.1, 244-284. (pdf, ps)
  111. Grigor'yan, A., Telcs, A. Harnack inequalities and sub-Gaussian estimates for random walks, Math. Annalen 324 (2002) no.3, 521-556. (pdf)
  112. Coulhon, T., Grigor'yan, A. Pointwise estimates for transition probabilities of random walks on infinite graphs, in: "Trends in Mathematics: Fractals in Graz 2001". Ed. P.Grabner and W.Woess. Birkhäuser 2002. 119-134. (pdf, ps)
  113. Grigor'yan, A., Saloff-Coste, L. Hitting probabilities for Brownian motion on Riemannian manifolds, J.  Math. Pures  Appl. 81 (2002) 115-142. (pdf, ps)
  114. Grigor'yan, A., Saloff-Coste, L. Dirichlet heat kernel in the exterior of a compact set, Comm. Pure Appl. Math. 55 (2002) 93-133. (pdf, ps)
  115. Grigor'yan, A., Telcs, A. Sub-Gaussian estimates of heat kernels on infinite graphs, Duke Math. J. 109 (2001) no.3, 451-510. (pdf, ps) Correction to Section 10 (pdf, ps) 
  116. Coulhon, T., Grigor'yan, A., Pittet, Ch. A geometric approach to on-diagonal heat kernel lower bounds on groups, Ann. Inst. Fourier, Grenoble 51 (2001) no.6, 1763-1827. (pdf, ps)
  117. Barlow, M., Coulhon, T., Grigor'yan, A. Manifolds and graphs with slow heat kernel decay,  Invent. Math. 144 (2001) 609-649. (pdf, ps)
  118. Grigor'yan, A., Kelbert, M. Asymptotic separation for independent trajectories of Markov processes, Prob. Th. Rel. Fields, 119 (2001) no.1, 31-69. (pdf, ps)
  119. Grigor'yan, A., Heat kernels on manifolds, graphs and fractals,  in: "European Congress of Mathematics: Barcelona, July 10-14, 2000; Volume I",  Progress in Mathematics 201  Birkhäuser 2001. p.393-406. (pdf, ps)
  120. ed. A. Fokas, A. Grigor'yan, T. Kibble, B. Zegarlinski, "XIII-th International Congress of Mathematical Physics. Imperial College, London, UK, July 17-22, 2000", International Press, 2001.
  121. ed. A. Fokas, A. Grigor'yan, T. Kibble, B. Zegarlinski, "Mathematical Physics 2000", Imperial College Press, 2000.
  122. Chung, F. R. K., Grigor'yan, A., Yau, S.-T. Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs, Comm. Anal. Geom. 8 (2000) no.5, 969-1026 (pdf, ps)
  123. Grigor'yan, A., Kelbert, M. On Hardy-Littlewood inequality for Brownian motion on Riemannian manifold, Journal of LMS, 69 (2000) 625-639. (pdf, ps)
  124. Grigor'yan, A., Hansen, W. Lower estimates for perturbed Dirichlet solutions, unpublished manuscript, 2000. (pdf, ps, dvi) 
  125. Grigor'yan, A., Saloff-Coste, L. Heat kernel on connected sums of Riemannian manifolds Math. Research Letters 6 (1999) 307-321. (pdf, ps, dvi)
  126. Grigor'yan, A. Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bulletin of Amer. Math. Soc. 36 (1999) 135-249. (pdf)
  127. Grigor'yan, A. Estimates of heat kernels on Riemannian manifolds, in "Spectral Theory and Geometry. ICMS Instructional Conference, Edinburgh, 1998", ed. B. Davies and Yu. Safarov, Cambridge Univ. Press, London Math. Soc. Lecture Notes 273 (1999) 140-225. (pdf, ps)
  128. Grigor'yan, A. Isoperimetric inequalities and capacities on Riemannian manifolds, Operator Theory: Advances and Applications, 109 (1999)  139-153 "V. G. Maz'ya Birthday Volume". (pdf, ps, dvi)
  129. Grigor'yan, A. Escape rate of Brownian motion on Riemannian manifolds, Applicable Analysis 7 (1999) 63-89 "E. M. Landis Memorial Volume" (pdf)
  130. Grigor'yan, A., Yau S.-T. Decomposition of a metric space by capacitors, Proceeding of Symposia in Pure Mathematics 65 (1999) 39-75. "L. Nirenberg Birthday Volume" (pdf)
  131. Coulhon, T. and Grigor'yan, A. Random walks on graphs with regular volume growth, Geom. and Funct. Anal. 8 (1998) 656-701.(pdf, ps)
  132. Grigor'yan, A., Hansen, W. Liouville property for a Schrödinger operator, Math. Ann. 312 (1998) 659-716. (pdf)
  133. Grigor'yan, A., Noguchi, M. The heat kernel on hyperbolic space, Bulletin of LMS, 30 (1998) 643-650 (pdf, ps, dvi)
  134. Grigor'yan, A., Kelbert, M. Range of fluctuation of Brownian motion on a complete Riemannian manifold, Annals of Probability 26 (1998) 78-111. (pdf, ps)
  135. Coulhon, T., Grigor'yan, A., On-diagonal lower bounds for heat kernels and Markov chains, Duke Math. J. 89 (1997) 133-199 (pdf, ps, dvi)
  136. Grigor'yan, A., Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Diff. Geom. 45 (1997) 33-52 (pdf, ps, dvi)
  137. Chung, F. R. K., Grigor'yan, A., Yau S.-T., Eigenvalues and diameters for manifolds and graphs, in: "Tsing Hua Lectures on Geometry and Analysis", ed. S.-T. Yau, International Press, 1997. p.79-105. (pdf, ps, dvi)
  138. Coulhon, T., Grigor'yan, A., Heat kernel, volume growth and anti-isoperimetric inequalities, C.R. Acad. Sci. Paris, 322 (1996) pp.1027-1032 (pdf, ps, dvi)
  139. Chung, F. R. K., Grigor'yan, A., Yau S.-T., Upper bounds for eigenvalues of the discrete and continuous Laplace operators, Advances in Math. 117 (1996) 165-178. (pdf, ps, dvi)
  140. Grigor'yan, A., Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold, J. Funct. Anal. 127 (1995), no.2, 363-389.  (pdf, ps, dvi)
  141. Grigor'yan, A., Heat kernel on a non-compact Riemannian manifold, Proceedings of Symposia in Pure Mathematics, 57 (1995), 239-263. (pdf, ps, dvi)
  142. Grigor'yan, A., Gaussian upper bounds for the heat kernel and for its derivatives on a Riemannian manifold, in "Proceeding of the ARW on Potential Theory, Chateau de Bonas, July 1993", ed. K.GowriSankaran, Kluwer Academic Publisher, 1994. 237-252. (pdf, ps, dvi)
  143. Grigor'yan, A., Heat kernel on a manifold with a local Harnack inequality, Comm. Anal. Geom., 2 (1994) no.1, 111-138. (pdf, ps, dvi)
  144. Grigor'yan, A., Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoam. 10 (1994) no.2, 395-452. (pdf, ps, dvi)
  145. Grigor'yan, A., Integral maximum principle and its applications , Proc. of Edinburgh Royal Soc. 124A (1994) 353-362. (pdf, ps, dvi)
  146. Grigor'yan, A., The heat equation on non-compact Riemannian manifolds, Math. USSR Sb. 72 (1992) no.1, 47-77. (pdf) Translated from Russian: Matem. Sbornik, 182 (1991), no.1, 55-87. Abstract: "Harnack inequality for the heat equation" (pdf, dvi)
  147. Grigor'yan, A., Dimension of spaces of harmonic functions, Math. Notes  48 (1990) no. 5, 1114-1118. (pdf) Translated from Russian: Matem. Zametki 48 (1990) no.5, 55-61.
  148. Grigor'yan, A., Bounded solutions of the Schrödinger equation on non-compact Riemannian manifolds, J. Soviet Math. 51 (1990) no.3, 2340-2349. (pdf) Translated from Russian: Trudy seminara I.G.Petrovskogo  (1989) no.14, 66-77.
  149. Grigor'yan, A., Stochastically complete manifolds and summable harmonic functions,  Math. USSR Izvestiya  33 (1989) no.2, 425-432. (pdf)  Translated from Russian: Izv. AN SSSR, ser. matem. 52 (1988) no.5, 1102-1108.
  150. Grigor'yan, A., On Liouville theorems for harmonic functions with finite Dirichlet integral, Math. USSR Sbornik 60 (1988) no.2, 485-504. (pdf) Translated from Russian: Matem. Sbornik 132 (1987) no.4, 496-516.
  151. Grigor'yan, A., A criterion for the existence on a Riemannian manifold of a nontrivial bounded harmonic function with a finite Dirichlet integral, Soviet Math. Dokl. 35 (1987) no.2, 339-341. Translated from Russian: Dokl. Akad. Nauk SSSR 293 (1987) no.3, 529-531.
  152. Grigor'yan, A., On the set of positive solutions of Laplace-Beltrami equation on special type of Riemannian manifolds, Soviet Math (Iz.VUZ) 31 (1987) no.2, 48-60. (pdf) Translated from Russian: Izv. Vyssh. Uchebn. Zaved.,  Matematika (1987) no.2, 30-37.
  153. Grigor'yan, A., Nadirashvili, N.S., The Liouville theorems and exterior boundary value problems, Soviet Math. (Iz.VUZ) 31 (1987) no.5, 31-42. (pdf)  Translated from Russian: Izv. Vyssh. Uchebn. Zaved., Matematika (1987) no.5, 25-33.
  154. Grigor'yan, A., On the fundamental solution of the heat equation on an arbitrary Riemannian manifold, Math. Notes  41 (1987) no.5-6, 386-389. (pdf)  Translated from Russian: Matem. Zametki  41 (1987) no.3, 687-692.
  155. Grigor'yan, A., Stochastically complete manifolds, Soviet Math. Dokl  34 (1987) no.2, 310-313 (pdf)  Translated from Russian: DAN SSSR  290 (1986) no.3, 534-537.
  156. Grigor'yan, A., The existence of positive fundamental solution of the Laplace equation on Riemannian manifolds, Math. USSR Sb. 56 no.2 (1987)  349-358 (pdf)  Translated from Russian: Matem. Sbornik 128 (1985), no.3, 354-363.
  157. Grigor'yan, A., Isoperimetric inequalities for Riemannian products, Math. Notes 38 (1985) 849-854 (pdf) Translated from Russian: Matem. Zametki 38 (1985) no.4, 617-626.
  158. Grigor'yan, A., Existence of the Green function on a manifold,  Russian Math. Surveys 38 (1983) no.1, 190-191. Translated from Russian: Uspekhi Matem. Nauk 38 (1983) no.1, 161-162 (pdf)
  159. Grigor'yan, A., A Liouville theorem on a Riemannian manifold (in Russian), Trudy Tbiliss. Univ. ser. matem., 232/233 (1982) 49-77.
  160. Grigor'yan, A., A Liouville theorem on a manifold, Russian Math. Surveys 37 (1982)  no.3, 209-210. Translated from Russian: Uspekhi Matem. Nauk 37 (1982) no.3, 181-182 (pdf)
  161. Grigor'yan, A., On the connection of orders with which the solutions of second-order homogeneous elliptic equations in unbounded domains tend to +∞ and −∞, Moscow Univ. Math. Bull., 34 (1979) no.5, 35-43. Translated from Russian: Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1979) no.5, 32-38.