Preprints

• G. Claret, M. Hinz, A. Rozanova-Pierrat, A. Teplyaev, 'Layer potential operators for transmission problems on extension domains', preprint (2024), hal-04505158.

• S. Creo, M. Hinz, M.R. Lancia, 'Non-local boundary energy forms for quasidiscs: Codimension gap and approximation', preprint (2023), arXiv:2310.04549.

• P. Alonso-Ruiz, M. Hinz, A. Teplyaev, R. Treviño, 'Canonical diffusions on the pattern spaces of aperiodic Delone sets', preprint (2018), arXiv:1801.08956.

Publications

• M. Hinz, J. Kommer, 'A tensor product approach to non-local differential complexes', Math. Ann. (2023), https://doi.org/10.1007/s00208-023-02703-w

• M. Hinz, J. Masamune, K. Suzuki, 'Removable sets and Lp-uniqueness on manifolds and metric measure spaces', Nonlin. Anal. 234 (2023), 113296.

• S. Alikhanloo, M. Hinz, 'Self-adjoint Laplacians and symmetric diffusions on hyperbolic attractors', J. London Math. Soc. 107 (6) (2023), 1925-1958.

• M. Hinz, A. Rozanova-Pierrat, A. Teplyaev, 'Boundary value problems on non-Lipschitz uniform domains: Stability, compactness and the existence of optimal shapes', Asympt. Anal. 134 (2023), 25-61.

• M. Hinz, J. Tölle, L. Viitasaari, 'Variability of paths and differential equations with BV-coefficients', Ann. Inst. H. Poincaré Probab. Statist. 59 (4) (2023), 2036-2082.

• M. Hinz, J. Tölle, L. Viitasaari, 'Sobolev regularity of occupation measures and paths, variability and compositions', Electron. J. Probab. 27 (2022), 1-29.

• M. Hinz, M. Schwarz, 'A note on Neumann problems on graphs', Positivity 26, 68 (2022).

• M. Hinz, M. Meinert, 'Approximation of partial differential equations on compact resistance spaces', Calc. Var. PDE 61, 19 (2022).

• M. Hinz, F. Magoulès, A. Rozanova-Pierrat, M. Rynkovskaya, A. Teplyaev, 'On the existence of optimal shapes in architecture', Appl. Math. Model. 94 (2021), 676-687.

• M. Hinz, A. Rozanova-Pierrat, A. Teplyaev, 'Non-Lipschitz uniform domain shape optimization in linear acoustics', SIAM J. Control. Optim. 59 (2) (2021), 1007-1032.

• M. Hinz, S. Kang, 'Capacities, removable sets and Lp-uniqueness on Wiener spaces', Potential Anal. 54 (3) (2021), 503-533.

• S. Creo, M. Hinz, M.R. Lancia, A. Teplyaev, P. Vernole, 'Magnetostatic problems in fractal domains', in: 'Analysis, Probability and Mathematical Physics on Fractals', World Scientific, 2020, arXiv:1805.08262.

• M. Hinz, D. Koch, M. Meinert, 'Sobolev spaces and calculus of variations on fractals', in: 'Analysis, Probability and Mathematical Physics on Fractals', World Scientific, 2020, arXiv:1805.04456.

• M. Hinz, M. Meinert, 'On the viscous Burgers equation on metric graphs and fractals', J. Fractal Geometry 7 (2) (2020), 137-182.

• J.P. Chen, M. Hinz, A. Teplyaev, 'From non-symmetric particle systems to non-linear PDEs on fractals', In: 'Stochastic Partial Differential Equations and Related Fields – In Honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 – 14, 2016', Springer Proc. Math. & Stat. 229, 2018, pp. 503-513.

• M. Hinz, A. Teplyaev, 'Densely defined non-closable curl on carpet-like metric measure spaces', Math. Nachr. 291 (11-12) (2018), 1743-1756.

• M. Hinz, M.R. Lancia, A. Teplyaev, P. Vernole, 'Fractal snowflake domain diffusion with boundary and interior drifts', J. Math. Anal. Appl. 457 (1) (2018), 672-693.

• M. Hinz, S. Kang, J. Masamune, 'Probabilistic characterizations of essential self-adjointness and removability of singularities', Sci. Journal of Volgograd State Univ. Math. Physics and Comp. Sim. 2017 (3) (40) (2017), 148-162.

• M.L. Bedini, M. Hinz, 'Credit default prediction and parabolic potential theory', Stat. Probab. Letters 124 (2017), 121-125.

• M. Hinz, 'Sup-norm-closable bilinear forms and Lagrangians', Ann. Mat. Pura Appl. 195 (4) (2016), 1021-1054.

• M. Hinz, L. Rogers, 'Magnetic fields on resistance spaces', J. Fractal Geometry 3 (2016), 75-93.

• M. Hinz, A. Teplyaev, 'Closability, regularity, and approximation by graphs for separable bilinear forms', Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 441 (Veroyatnost i Statistika. 22) (2015), 299-317, reprint in J. Math. Sci. 219 (5) (2016), 807-820.

• M. Hinz, 'Magnetic energies and Feynman-Kac-Itô formulas for symmetric Markov processes', Stoch. Anal. Appl. 33 (6) (2015), 1020-1049.

• M. Hinz, A. Teplyaev, 'Finite energy coordinates and vector analysis on fractals', Progress in Probability 70, Fractal Geometry and Stochastics V, Birkhäuser, 2015, pp. 209-227.

• M. Hinz, D. Kelleher, A. Teplyaev, 'Metrics and spectral triples for Dirichlet and resistance forms', J. Noncomm. Geometry 9 (2) (2015), 359-390.

• M. Hinz, A. Teplyaev, 'Local Dirichlet forms, Hodge theory, and the Navier-Stokes equation on topologically one-dimensional fractals', Trans. Amer. Math. Soc. 367 (2015), 1347-1380. Corrected version: arXiv:1206.6644, Corrigendum: Trans. Amer. Math. Soc. 369 (2017), 6777-6778.

• M. Hinz, 'Magnetic energies and Feynman-Kac formulas based on regular Dirichlet forms', extended abstract in: Oberwolfach Reports vol. 11 (4) (2014), Report No. 48/2014, pp. 2731-2733.

• M. Hinz, D. Kelleher, A. Teplyaev, 'Measures and Dirichlet forms under the Gelfand transform', Zap. Nauchn. Sem. (POMI) 408 (2012), 303-322, reprint in J. Math. Sciences 199 (2) (2014), 236-246.

• M. Hinz, E. Issoglio, M. Zähle, 'Elementary pathwise methods for nonlinear parabolic and transport type SPDE with fractal noise', in: Modern Stochastics and Applications, Springer Optimization and Its Applications, Volume 90, 2014, pp. 123-141.

• M. Hinz, '1-forms, vector fields, and topologically one-dimensional fractals', extended abstract in: Oberwolfach Reports vol. 10 (2) (2013), Report No. 23/2013, pp. 1423-1426.

• M. Hinz, M. Röckner, A. Teplyaev, 'Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces', Stoch. Proc. Appl. 123 (12) (2013), 4373-4406.

• M. Hinz, A. Teplyaev, 'Dirac and magnetic Schrödinger operators on fractals', J. Funct. Anal. 265 (11) (2013), 2830-2854.

• M. Hinz, A. Teplyaev, 'Vector analysis on fractals and applications', Contemp. Math. 601 (2013), 147-163.

• M. Hinz, '1-forms and polar decomposition on harmonic spaces', Potential Anal. 38 (1) (2013), 261-279.

• M. Hinz, M. Zähle, 'Semigroups, potential spaces and applications to (S)PDE', Potential Anal. 36 (3) (2012), 483-515.

• M. Hinz, 'Limit chains on the Sierpinski gasket', Indiana Univ. Math. J. 60 (2011), 1797-1830.

• M. Hinz, 'Jump processes on spaces with non-uniform volume growth', Kyushu J. Math. 65 (2) (2011), 395-415.

• M. Hinz, 'Burgers system with a fractional Brownian random force', Stochastics 83 (1) (2011), 67-106.

• M. Hinz, 'Stochastic partial differential equations with fractal noise', In: 'Stochastic Analysis and Random Dynamical Systems', Lviv, Ukraine, 2009.

• M. Hinz, M. Zähle, 'Gradient type noises II – systems of stochastic partial differential equations', J. Funct. Anal. 256 (2009), 3192-3235.

• M. Hinz, M. Zähle, 'Gradient type noises I – hybrid integrals', Compl. Var. Ell. Eq. 54 (2009), 561-583.

• M. Hinz, 'Approximation of jump processes on fractals', Osaka J. Math. 46 (2009), 141-171.

• M. Hinz, 'Approximation of jump processes on fractals', extended abstract in: Oberwolfach Reports vol. 4 (2) (2007), Report No. 19/2007, pp. 1050-1052.

Theses

• M. Hinz, 'First order calculus for Dirichlet forms – Analytic and probabilistic aspects', Habilitation thesis, Bielefeld University, 2019.

• M. Hinz, 'Stochastic partial differential equations with fractal noise' , Dissertation, FSU Jena, 2009.

• M. Hinz, 'Average densities and limits of potentials', Diploma thesis, FSU Jena, 2005.

Edited volumes

• 'Fractal Geometry and Stochastics VI', U. Freiberg, B. Hambly, M. Hinz, S. Winter, editors, Progress in Probability 76, Birkhäuser, Basel, 2021.

• 'From Classical Analysis to Analysis on Fractals – Robert Strichartz Memorial Volume', P. Alonso-Ruiz, M. Hinz, K. Okoudjou, L. Rogers, A. Teplyaev, editors, Birkhäuser, 2023.