English

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}
}