Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization


Mcintyre, Andrew and Teo, Lee-Peng (2008) Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization. Letters in Mathematical Physics, 83 (1). pp. 41-58. ISSN 0377-9017

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For a quasi-Fuchsian group Gamma with ordinary set Omega, and Delta(n) the Laplacian on n-differentials on Gamma\Omega, we define a notion of a Bers dual basis phi(1),...,phi(2d) for ker Delta(n). We prove that det Delta(n)/det <phi(j), phi(k)>, is, up to an anomaly computed by Takhtajan and the second author in (Commun. Math Phys 239(1-2):183-240, 2003), the modulus squared of a holomorphic function F(n), where F(n) is a quasi-Fuchsian analogue of the Selberg zeta function Z(n). This generalizes the D'Hoker-Phong formula det Delta(n) = c(g,n) Z(n), and is a quasi-Fuchsian counterpart of the result for Schottky groups proved by Takhtajan and the first author in Analysis 16, 1291-1323, 2006.

Item Type: Article
Subjects: T Technology > T Technology (General)
Q Science > QC Physics
Divisions: Faculty of Engineering and Technology (FET)
Depositing User: Ms Suzilawati Abu Samah
Date Deposited: 21 Sep 2011 07:31
Last Modified: 13 Feb 2014 08:17
URII: http://shdl.mmu.edu.my/id/eprint/2876


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