Preprints
M. Hinz, W. Schefer, 'On equations of continuity and transport type on metric graphs and fractals', preprint (2024), arXiv:2412.07988.
M. Hinz, A. Pachon, 'Phase transition in preferential attachment-detachment through embedding', preprint (2024), arXiv:2410.09974.
M. Hinz, J. Kommer, 'Differential complexes for local Dirichlet spaces, and non-local-to-local approximations', preprint (2024), arXiv:2407.07252.
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. Tölle, L. Viitasaari, 'Variability and the existence of rough integrals with irregular coefficients', Electron. Comm. Probab. 30 (2025), paper 7, 1-12.
M. Hinz, J. Kommer, 'A tensor product approach to non-local differential complexes', Math. Ann. 389 (2024), 2357-2409.
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.