Boundary fibration structures and quasi-homogeneous geometries
Abstract/Contents
- Abstract
- In this thesis we extend work by Mazzeo on conformally compact manifolds to a class of manifolds with quasi-homogeneous geometries, which we call kappa-manifolds. Our results show that there are complete noncompact manifolds of negative curvature, that have 0 in the essential spectrum for the Hodge Laplacian on forms, and this applies in a range of degrees centered at the middle degree. As is typical for boundary fibration structures our methods give much more, namely we provide a general framework to study elliptic partial differential operators on kappa-manifolds based on microlocal methods. We construct a calculus of pseudodifferential operators on the manifold, and give precise conditions for the existence of a parametrix for elliptic differential operators in this calculus. This work takes up the bulk of the thesis. We then apply this to the spectral theory of the Hodge Laplacian on a kappa-manifold. This step requires detailed analysis of the Hodge Laplacian on a simpler model space, which in turn requires detailed study of a system of ordinary differential equations.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Thorvaldsson, Sverrir |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Mazzeo, Rafe |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Vasy, András |
| Thesis advisor | Zhu, Xuwen, 1988- |
| Advisor | Vasy, András |
| Advisor | Zhu, Xuwen, 1988- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Sverrir Thorvaldsson. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Sverrir Orn Thorvaldsson
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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