Geometric variational problems in mathematical physics
Abstract/Contents
- Abstract
- We study two different geometrically flavored variational problems in mathematical physics: quasi-local mass in the initial data set approach to the general theory of relativity, and the theory of phase transitions. In the general relativity setting, we introduce a new moduli space of metrics on spheres and a new metric invariant on surfaces to help obtain a precise local understanding of the interaction of ambient scalar curvature and stable minimal surfaces in the context of three-manifolds with nonnegative scalar curvature; we use these tools to study the Bartnik and Brown-York notions quasi-local mass in general relativity. In the theory of phase transitions, we study the global behavior of two-dimensional solutions, and relate their complexity at infinity to their variational instability.
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 | Mantoulidis, Christos Apostolos |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Schoen, Richard (Richard M.) |
| Primary advisor | White, Brian, 1957- |
| Thesis advisor | Schoen, Richard (Richard M.) |
| Thesis advisor | White, Brian, 1957- |
| Thesis advisor | Simon, L. (Leon), 1945- |
| Advisor | Simon, L. (Leon), 1945- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Christos Apostolos Mantoulidis. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Christos Apostolos Mantoulidis
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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