Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits

2025/01/13 by Ellen Krusell, Krusell, Ellen · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Curvilinear coordinates #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Mathematics #Spectral Theory (math.SP) #math-ph #math.DG #math.SP

paper · pdf · doi:10.48550/arxiv.2501.07682

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/01/13 · arxiv published 2025/01/13 · arxiv updated 2025/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the ζ-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 ζ-regularized determinant of the Laplacian and prove a comparison formula of Polyakov-Alvarez type for a smooth and conformal change of metric.

Cited by

• On the spectral geometry of Liouville quantum gravity

Discussions

• Ellen Krusell: Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits https://arxiv.org/abs/2501.07682 https://arxiv.org/pdf/2501.07682 https://arxiv.org/html/2501.07682 [bsky, 0 points, 1 comments]

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