The heat kernel on curvilinear polygonal domains in surfaces
Nursultanov M. Rowlett J. Sher D.
April 2025Springer Science and Business Media Deutschland GmbH
Annales Mathematiques du Quebec
2025#49Issue 11 - 61 pp.
We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic expansion of the heat trace and apply this expansion to demonstrate a collection of results showing that corners are spectral invariants.
Conic singularity , Corner , Curvilinear polygon , Dirichlet boundary condition , Edge , Heat kernel , Heat trace , Inverse spectral problem , Isospectral , Mixed boundary conditions , Neumann boundary condition , Robin boundary condition , Spectral invariant , Spectrum , Surface with corners , Vertex , Zaremba boundary condition
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Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Mathematical Sciences, Chalmers University and the University of Gothenburg, Gothenburg, 412 96, Sweden
Department of Mathematical Sciences, DePaul University, 2320 N Kenmore Ave, Chicago, 60614, IL, United States
Department of Mathematics and Statistics
Institute of Mathematics and Mathematical Modeling
Mathematical Sciences
Department of Mathematical Sciences
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