On the free-boundary mean curvature flow
Abstract/Contents
- Abstract
- We investigate the free-boundary mean curvature flow. This is an evolution of surfaces by "steepest descent for area,'' while preserving the Neumann-type condition that all the surfaces meet some fixed barrier orthogonally. For example, a bubble in a sink. We first prove the Huisken-Sinestrari convexity estimates for free-boundary mean curvature flow, which classifies "type-II'' singularities. We then develop the notion of weak free-boundary mean curvature flow, extending Brakke's original definition, and proving a local regularity theorem. We also prove a geometric eigenvalue gap estimate, extending results of Ashbaugh-Benguria and Benguria-Linde.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Edelen, Nicholas |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Brendle, Simon, 1981- |
| Primary advisor | White, Brian T, 1963- |
| Thesis advisor | Brendle, Simon, 1981- |
| Thesis advisor | White, Brian T, 1963- |
| Thesis advisor | Simon, L. (Leon), 1945- |
| Advisor | Simon, L. (Leon), 1945- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Nicholas Edelen. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Nicholas Sumner Edelen
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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