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arXiv · 1905.00259

The heat kernel on curvilinear polygonal domains in surfaces

Medet Nursultanov·Julie Rowlett·David A. Sher
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Abstract

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.

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Medet Nursultanov, Julie Rowlett, David A. Sher. 2019-05-01. The heat kernel on curvilinear polygonal domains in surfaces. https://doi.org/10.1007/s40316-024-00237-4

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