Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians

dc.creatorKlochko, Yulia
dc.creatorKokotov, Alexey
dc.date2006-05-23
dc.date2006-07-12
dc.date.accessioned2026-07-07T07:14:28Z
dc.date.available2026-07-07T07:14:28Z
dc.descriptionWe 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.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0605614
dc.identifierhttp://arxiv.org/abs/math/0605614
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112889
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.titleGenus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians
dc.typetext

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