Applications of microlocal analysis in general relativity and inverse problems
Abstract/Contents
- Abstract
- This thesis consists of three parts: the first part serves as a brief introduction to microlocal analysis; the second part is the application of microlocal analysis in general relativity; the third part is the application of microlocal analysis in inverse problems. In the first part, we introduce various pseudodifferential operator algebras we will use as tools in our applications. These algebras include well-known ones such as classical, scattering and balgebras, and also relatively new ones such as 1-cusp (in fact, its semiclassical foliation version) and the one we construct for our wave propagation on Kerr(-de Sitter) spacetimes. In the second part, we prove a propagation estimate with arbitrarily small extra loss compared with the classical non-trapping propagation estimates using the algebra we constructed in Chapter 3. One of the major applications of estimates of this type is to linearized Einstein equations on the Kerr(-de Sitter) spacetimes. In the third part, we consider the injectivity of the X-ray transform on one forms and 2-tensors on asymptotically conic manifolds. This uses the algebra developed by Andras Vasy and Evangelie Zachos. This question is motivated by the boundary rigidity problem of asymptotically conic manifolds, we expect this injectivity result of the X-ray transform to be a linearization of it and serve as a key ingredient in the proof of this rigidity problem.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Jia, Qiuye | |
|---|---|---|
| Degree supervisor | Vasy, András | |
| Thesis advisor | Vasy, András | |
| Thesis advisor | Mazzeo, Rafe | |
| Thesis advisor | Ryzhik, Leonid | |
| Degree committee member | Mazzeo, Rafe | |
| Degree committee member | Ryzhik, Leonid | |
| Associated with | Stanford University, School of Engineering | |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Qiuye Jia. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/yc828ws1049 |
Access conditions
- Copyright
- © 2023 by Qiuye Jia
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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