Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization
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 t...
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SPRINGER
2008
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| Online Access: | http://shdl.mmu.edu.my/2876/ http://shdl.mmu.edu.my/2876/1/910.pdf |
| _version_ | 1848790173778706432 |
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| author | Mcintyre, Andrew Teo, Lee-Peng |
| author_facet | Mcintyre, Andrew Teo, Lee-Peng |
| author_sort | Mcintyre, Andrew |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:08:25Z |
| format | Article |
| id | mmu-2876 |
| institution | Multimedia University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:08:25Z |
| publishDate | 2008 |
| publisher | SPRINGER |
| recordtype | eprints |
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| spelling | mmu-28762014-02-13T08:17:29Z http://shdl.mmu.edu.my/2876/ Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization Mcintyre, Andrew Teo, Lee-Peng T Technology (General) QC Physics 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. SPRINGER 2008-01 Article NonPeerReviewed text en http://shdl.mmu.edu.my/2876/1/910.pdf 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 http://dx.doi.org/10.1007/s11005-007-0204-9 doi:10.1007/s11005-007-0204-9 doi:10.1007/s11005-007-0204-9 |
| spellingShingle | T Technology (General) QC Physics Mcintyre, Andrew Teo, Lee-Peng Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| title | Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| title_full | Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| title_fullStr | Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| title_full_unstemmed | Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| title_short | Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization |
| title_sort | holomorphic factorization of determinants of laplacians using quasi-fuchsian uniformization |
| topic | T Technology (General) QC Physics |
| url | http://shdl.mmu.edu.my/2876/ http://shdl.mmu.edu.my/2876/ http://shdl.mmu.edu.my/2876/ http://shdl.mmu.edu.my/2876/1/910.pdf |