The vacuum Einstein constraint equations on manifolds with ends of cylindrical type
Abstract/Contents
- Abstract
- This dissertation concerns the vacuum Einstein constraint equations on manifolds possessing end regions which are asymptotically periodic, including the special case where the ends are conformally asymptotically cylindrical. We will first apply the conformal method to construct a large class of vacuum initial data on any such manifold with positive Yamabe invariant, and then extend these existence results to manifolds which may also have asymptotically Euclidean ends. We will also show that, in the conformally asymptotically cylindrical case, any solution to the constraints one obtains via the conformal method which preserves the end geometry must have a unique asymptotic limit. Finally, we describe two different approaches to gluing generic asymptotically periodic initial data sets end-to-end, thereby allowing us to construct a large family of initial data sets with ``long neck'' regions.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Leach, Jeremy |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Mazzeo, Rafe |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Schoen, Richard (Richard M.) |
| Thesis advisor | Vasy, András |
| Advisor | Schoen, Richard (Richard M.) |
| Advisor | Vasy, András |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jeremy Leach. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Jeremy Jonathan Leach
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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