The heat kernel on curvilinear polygonal domains in surfaces
Artikel i vetenskaplig tidskrift, 2024
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.
Edge
Neumann boundary condition
Isospectral
Heat kernel
Conic singularity
Mixed boundary conditions
Robin boundary condition
Spectrum
Vertex
Heat trace
Zaremba boundary condition
Inverse spectral problem
Surface with corners
Corner
Curvilinear polygon
Dirichlet boundary condition
Spectral invariant
Författare
Medet Nursultanov
Helsingin Yliopisto
Al Farabi Kazakh National University
Julie Rowlett
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori
David Sher
DePaul University
Annales Mathematiques du Quebec
21954755 (ISSN) 21954763 (eISSN)
Vol. In PressGeometrisk analys och tillämpningar i mikrobekologi
Vetenskapsrådet (VR) (2018-03873), 2019-01-01 -- 2022-12-31.
Ämneskategorier (SSIF 2011)
Matematisk analys
DOI
10.1007/s40316-024-00237-4