Zeta Determinant for Laplace Operators on Riemann Caps

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 $D-$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.

19 pages, 1 figure

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• Casimir effect in hemisphere capped tubes
• Asymptotic Expansion of the Heat Kernel Trace of Laplacians with Polynomial Potentials
• Representations for the derivative at zero and finite parts of the Barnes zeta function
• Heat Kernel Asymptotic Expansion on Unbounded Domains with Polynomially Confining Potentials