Holomorphic Extensions of Laplacians and Their Determinants
| dc.creator | Kim, Young-Heon | |
| dc.date | 2005-05-25 | |
| dc.date.accessioned | 2026-07-07T05:20:15Z | |
| dc.date.available | 2026-07-07T05:20:15Z | |
| dc.description | The Teichmueller space Teich(S) of a surface S in genus g>1 is a totally real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det'(Δ) on Teich(S) has a unique holomorphic extension to QF(S). To realize this holomorphic extension as the determinant of differential operators on S, we introduce a holomorphic family {Δ_{μ,ν}} of elliptic second order differential operators on S whose parameter space is the space of pairs of Beltrami differentials on S and which naturally extends the Laplace operators of hyperbolic metrics on S. We study the determinant of this family {Δ_{μ,ν}} and show how this family realizes the holomorphic extension of det'(Δ) as its determinant. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505530 | |
| dc.identifier | http://arxiv.org/abs/math/0505530 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75310 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32G15; 58J52 | |
| dc.title | Holomorphic Extensions of Laplacians and Their Determinants | |
| dc.type | text |