Diffusion determines the manifold

DOI10.1515/CRELLE.2011.131zbMath1260.58016arXiv0806.0437OpenAlexW2963372948MaRDI QIDQ2898921

Markus Biegert, A. F. M. ter Elst, Wolfgang Arendt

Publication date: 12 July 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.0437

zbMATH Keywords

semigroupheat diffusionlattice homomorphismorder isomorphismDirichlet Laplace-Beltrami operatorregular in capacity

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Isospectrality (58J53)

Related Items (8)

Ergodic decompositions of Dirichlet forms under order isomorphisms ⋮ Uniqueness of the approximative trace ⋮ On order isomorphisms intertwining semigroups for Dirichlet forms ⋮ Analysis of the heat kernel of the Dirichlet-to-Neumann operator ⋮ Diffusion determines the recurrent graph ⋮ Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups ⋮ Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients ⋮ Disjointness-preserving operators and isospectral Laplacians

Cites Work

• Unnamed Item
• Regularity in capacity and the Dirichlet Laplacian
• Varying domains: Stability of the Dirichlet and the Poisson problem
• Isospectral plane domains and surfaces via Riemannian orbifolds
• Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds
• The Laplacian with Robin boundary conditions on arbitrary domains
• Isospectral convex domains in Euclidean space
• Parabolic Harnack inequality for divergence form second order differential operators
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
• Can One Hear the Shape of a Drum?
• Spectral determination of analytic bi-axisymmetric plane domains

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