The heat kernel on curvilinear polygonal domains in surfaces
Journal article, 2025
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.
Mixed boundary conditions
Heat kernel
Spectrum
Heat trace
Dirichlet boundary condition
Corner
Robin boundary condition
Curvilinear polygon
Neumann boundary condition
Zaremba boundary condition
Isospectral
Spectral invariant
Vertex
Surface with corners
Conic singularity
Inverse spectral problem
Edge
Author
Medet Nursultanov
University of Helsinki
Al Farabi Kazakh National University
Julie Rowlett
University of Gothenburg
Chalmers, Mathematical Sciences, Analysis and Probability Theory
David Sher
DePaul University
Annales Mathematiques du Quebec
21954755 (ISSN) 21954763 (eISSN)
Vol. 49, 1 1-61Geometric analysis and applications to microbe ecology
Swedish Research Council (VR) (2018-03873), 2019-01-01 -- 2022-12-31.
Subject Categories (SSIF 2011)
Mathematical Analysis
DOI
10.1007/s40316-024-00237-4