Zeta Determinant for Laplace Operators on Riemann Caps
Mathematical Physics
2011-03-04 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Spectral Theory
Abstract
The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.
Keywords
Cite
@article{arxiv.1004.0063,
title = {Zeta Determinant for Laplace Operators on Riemann Caps},
author = {Antonino Flachi and Guglielmo Fucci},
journal= {arXiv preprint arXiv:1004.0063},
year = {2011}
}
Comments
19 pages, 1 figure