Conic degeneration and the determinant of the laplacian
Abstract/Contents
- Abstract
- We consider a family of smooth Riemannian manifolds which degenerate to a manifold with a conical singularity. Such families arise in various settings in spectral theory, including the study of the isospectral problem. We investigate the behavior of the determinant of the Laplacian under the degeneration. Our main result is an approximation formula for the determinant, including all terms which do not vanish in the limit. The key idea is a uniform parametrix construction for the heat kernel on the degenerating family of manifolds, which enables us to analyze the determinant via the heat trace. It becomes clear in the construction that we need to understand both the short-time and long-time behavior of the heat kernel on an asymptotically conic manifold. Using techniques of Melrose and building on previous work of Guillarmou and Hassell, we give a complete description of the asymptotic structure of this heat kernel in all spatial and temporal regimes.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Sher, David Alexander |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Mazzeo, Rafe |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Vasy, András |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Advisor | Vasy, András |
| Advisor | Venkatesh, Akshay, 1981- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | David A. Sher. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by David Alexander Sher
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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