Determinants of Laplacians on the space of conical metrics on the sphere

Author:
Hala Khuri King

Journal:
Trans. Amer. Math. Soc. **339** (1993), 525-536

MSC:
Primary 58G26

MathSciNet review:
1102890

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Abstract: On a compact surface with smooth boundary, the determinant of the Laplacian associated to a smooth metric on the surface (with Dirichlet boundary conditions if the boundary is nonempty) is a well-defined isospectral invariant. As a function on the moduli space of such surfaces, it is a smooth function whose boundary behavior in certain cases is well understood; see [OPS and K]. In this paper, we restrict ourselves to a certain class of singular metrics on closed surfaces called conical metrics. We show that the determinant of the associated Laplacian is still well defined and that it is a real analytic function on a suitably restricted subset of the space of conical metrics on the sphere.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1102890-7

Keywords:
Conical metrics,
determinants of Laplacians,
spectral geometry of conical metrics

Article copyright:
© Copyright 1993
American Mathematical Society