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The heat kernel on curvilinear polygonal domains in surfaces

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arxiv 1905.00259 v2 pith:KL2VILFI submitted 2019-05-01 math.AP math.SP

Medet Nursultanov , Julie Rowlett , David A. Sher This is my paper · ORCID
classification math.APmath.SP
keywords heatcurvilineardomainsexpansionkernelpolygonalsurfacesapply
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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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  1. Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons

    math.SP 2019-08 accept novelty 8.0 of 10

    Steklov eigenvalues of curvilinear polygons are asymptotically equal to explicit quasi-eigenvalues built from side lengths and angles, with errors tending to zero.

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