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Zeta regularized determinants for conic manifolds |
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| Authors: | Paul Loya Jinsung Park |
| Institution: | a Department of Mathematics, Binghamton University, Vestal Parkway East, Binghamton, NY 13902, USA b Division of Natural Science, New College of Florida, Sarasota, FL 34243, USA c School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul 130-722, Republic of Korea |
| Abstract: | We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant. |
| Keywords: | Zeta regularized determinants Conic manifolds Gluing formulae |
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