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arXiv · 2501.07682

Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits

Ellen Krusell
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Abstract

We consider the $\zeta$-regularized determinant of the Friedrichs extension of the Dirichlet Laplace-Beltrami operator on curvilinear polygonal domains with corners of arbitrary positive angles. In particular, this includes slit domains. We obtain a short time asymptotic expansion of the heat trace using a classical patchwork method. This allows us to define the $\zeta$-regularized determinant of the Laplacian and prove a comparison formula of Polyakov-Alvarez type for a smooth and conformal change of metric.

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Ellen Krusell. 2025-01-13. Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits. https://arxiv.org/abs/2501.07682

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