Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians

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.

References in corpus (2)

• Lyapunov exponents and Hodge theory
• Further results on Functional Determinants of Laplacians in Simplicial Complexes

Cited by in corpus (5)

• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
• A heat trace anomaly on polygons
• Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities
• Spectral determinants for twist field correlators
• Finite deficiency indices and uniform remainder in Weyl's law