Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians
Differential Geometry
2009-06-04 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0906.0717,
title = {Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians},
author = {Alexey Kokotov},
journal= {arXiv preprint arXiv:0906.0717},
year = {2009}
}