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

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