Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| |
Authors: | Andrew Mcintyre Lee-Peng Teo |
| |
Institution: | (1) Bennington College, One College Drive, Bennington, Vermont 05201, USA;(2) Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya, 63100 Selangor Darul Ehsan, Malaysia |
| |
Abstract: | For a quasi-Fuchsian group Γ with ordinary set Ω, and Δ
n
the Laplacian on n-differentials on Γ\Ω, we define a notion of a Bers dual basis for ker Δ
n
. We prove that det , 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 , 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.
|
| |
Keywords: | Holomorphic factorization Laplacian Period matrix Differentials Quasi-Fuchsian |
本文献已被 SpringerLink 等数据库收录! |
|