The heat kernel on curvilinear polygonal domains in surfaces
R\'esum\'e 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.
Authors
- Medet Nursultanov (ORCID: https://orcid.org/0000-0003-2447-940X)
- David A. Sher (ORCID: https://orcid.org/0009-0003-2478-1083)
- Julie Rowlett (ORCID: https://orcid.org/0000-0002-5724-3252)
Institutions
- DePaul University (US)
- Statistics Finland (FI)
- University of Helsinki (FI)
- Institute of Mathematics and Mathematical Modeling (KZ)
- Chalmers University of Technology (SE)
- University of Gothenburg (SE)
Publication Details
- Journal
- Annales mathématiques du Québec
- Published
- 2024-12-27
- DOI
- https://doi.org/10.1007/s40316-024-00237-4
- Citations
- 5
- Primary Topic
- advanced mathematical theories
- Type
- article
- Field-Weighted Citation Impact
- 0.89
Funders
- DePaul University
- Chalmers Tekniska Högskola
- Vetenskapsrådet
- Ministry of Education and Science of the Republic of Kazakhstan
- College of Science and Health