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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2504.17652 |
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| _version_ | 1866912766204313600 |
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| author | Kokotov, Alexey Korikov, Dmitrii |
| author_facet | Kokotov, Alexey Korikov, Dmitrii |
| contents | Let $X$ be a genus zero compact polyhedral surface (the Riemann sphere equipped with a flat conical metric $m$). We derive the variational formulas for the determinant of the Laplacian, ${\rm det}\,Δ^m$, on $X$ under infinitesimal variations of the positions of the conical points and the conical angles (i. e. infinitesimal variations of $X$ in the class of polyhedra with the same number of vertices). Besides having an independent interest, this derivation may serve as a somewhat belated mathematical counterpart of the well-known heuristic calculation of ${\rm det}\,Δ^m$ performed by Aurell and Salomonson in the 90-s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On an infinitesimal Polyakov formula for genus zero polyhedra Kokotov, Alexey Korikov, Dmitrii Spectral Theory Primary 58J52, 35P99, 30F10, 30F45, Secondary 32G15, 32G08 Let $X$ be a genus zero compact polyhedral surface (the Riemann sphere equipped with a flat conical metric $m$). We derive the variational formulas for the determinant of the Laplacian, ${\rm det}\,Δ^m$, on $X$ under infinitesimal variations of the positions of the conical points and the conical angles (i. e. infinitesimal variations of $X$ in the class of polyhedra with the same number of vertices). Besides having an independent interest, this derivation may serve as a somewhat belated mathematical counterpart of the well-known heuristic calculation of ${\rm det}\,Δ^m$ performed by Aurell and Salomonson in the 90-s. |
| title | On an infinitesimal Polyakov formula for genus zero polyhedra |
| topic | Spectral Theory Primary 58J52, 35P99, 30F10, 30F45, Secondary 32G15, 32G08 |
| url | https://arxiv.org/abs/2504.17652 |