Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913647732719616 |
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| author | Krusell, Ellen |
| author_facet | Krusell, Ellen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits Krusell, Ellen Mathematical Physics Differential Geometry Spectral Theory 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. |
| title | Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits |
| topic | Mathematical Physics Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2501.07682 |