Further results on Functional Determinants of Laplacians in Simplicial Complexes

Abstract

We investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extend earlier investigations of the determinants on smooth surfaces with smooth boundaries. The differences to the smooth case are: a) different ``interaction energies'' between pairs of conical singularities than one would expect from a naive extrapolation of the results for a smooth surface; and b) ``self-energies'' of the singularities.

Cited by in corpus (9)

• Faddeev-Popov determinant in 2-dimensional Regge gravity.
• Further functional determinants
• Functional integration on two dimensional Regge geometries
• Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities
• Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians
• Quantum Hall States and Conformal Field Theory on a Singular Surface
• Spectral determinant on Euclidean isosceles triangle envelopes of fixed area as a function of angles: absolute minimum and small-angle asymptotics
• Group theoretical derivation of Liouville action for Regge surfaces
• Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians