Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians

Details Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians

2009-06-03

arxiv.org/abs/0906.0717v1

Mathematics

Differential Geometry

Scientific paper

Compact polyhedral surfaces (or, equivalently, compact Riemann surfaces with conformal flat conical metrics) of an arbitrary genus are considered. After giving a short self-contained survey of their basic spectral properties, we study the zeta-regularized determinant of the Laplacian as a functional on the moduli space of these surfaces. An explicit formula for this determinant is obtained.

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