Variational formulas for determinant of Laplacian on higher genus polyhedral surface
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916744482783232 |
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| author | Korikov, Dmitrii Kokotov, Alexey |
| author_facet | Korikov, Dmitrii Kokotov, Alexey |
| contents | Let $X$ be a Riemann surface of genus $g\ge 1$ endowed with a flat conical metric $m$ and let ${\rm det}\,Δ$ be the $ζ$-regularized determinant of the Friedrichs Laplacian on $(X,m)$. We derive variational formulas for ${\rm det}\,Δ$ with respect to conical points and conical angles within a given conformal class. Integration of them leads to an explicit expression for ${\rm det}\,Δ$ up to moduli dependent factor. The latter, in principle, can be calculated via comparison of the above result with the well-known formulas for the case of flat conical metrics with trivial holonomy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational formulas for determinant of Laplacian on higher genus polyhedral surface Korikov, Dmitrii Kokotov, Alexey Differential Geometry Spectral Theory Primary 58J52, 35P99, 30F10, 30F45, Secondary 32G15, 32G08 Let $X$ be a Riemann surface of genus $g\ge 1$ endowed with a flat conical metric $m$ and let ${\rm det}\,Δ$ be the $ζ$-regularized determinant of the Friedrichs Laplacian on $(X,m)$. We derive variational formulas for ${\rm det}\,Δ$ with respect to conical points and conical angles within a given conformal class. Integration of them leads to an explicit expression for ${\rm det}\,Δ$ up to moduli dependent factor. The latter, in principle, can be calculated via comparison of the above result with the well-known formulas for the case of flat conical metrics with trivial holonomy. |
| title | Variational formulas for determinant of Laplacian on higher genus polyhedral surface |
| topic | Differential Geometry Spectral Theory Primary 58J52, 35P99, 30F10, 30F45, Secondary 32G15, 32G08 |
| url | https://arxiv.org/abs/2505.13369 |