Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians
| dc.creator | Klochko, Yulia | |
| dc.creator | Kokotov, Alexey | |
| dc.date | 2006-05-23 | |
| dc.date | 2006-07-12 | |
| dc.date.accessioned | 2026-07-07T07:14:28Z | |
| dc.date.available | 2026-07-07T07:14:28Z | |
| dc.description | We prove a formula for the determinant of Laplacian on an arbitrary compact polyhedral surface of genus one. This formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic quadratic differential on an elliptic surface is also considered. We study the determinant of Laplacian as a functional on the moduli space of meromorphic quadratic differentials with L simple poles and L simple zeros and derive formulas for variations of this functional w. r. t. natural coordinates on this moduli space. A new proof of the Troyanov theorem about flat conical metrics on compact Riemann surfaces of arbitrary genus is also given. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605614 | |
| dc.identifier | http://arxiv.org/abs/math/0605614 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112889 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians | |
| dc.type | text |