Zeta determinant for Laplace operators on Riemann caps

Antonino Flachi; Guglielmo Fucci

doi:10.1063/1.3545705

Zeta determinant for Laplace operators on Riemann caps

Antonino Flachi, Guglielmo Fucci

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Article number	023503
Journal	Journal of Mathematical Physics
Volume	52
Issue number	2
DOIs	https://doi.org/10.1063/1.3545705
Publication status	Published - 2011 Feb 3
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3545705

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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.",

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note = "Funding Information: The authors are grateful to Alexander Yu. Kamenshchick, Klaus Kirsten, Misao Sasaki, and Takahiro Tanaka for very useful discussions. AF. acknowledges the support of the Japanese Society for Promotion of Science through Contract Nos. 19GS0219 and 20740133. A. F. would like to express his gratitude to the Department of Mathematics at Baylor University for the kind hospitality at the time when this work was initiated. ",

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