On harmonic maps into conic surfaces
Abstract/Contents
- Abstract
- We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, where the target has non-positive gauss curvature and conic points with cone angles less than $2\pi$. For a homeomorphism $w$ of such a surface, we prove existence and uniqueness of minimizers in the homotopy class of $w$ relative to the inverse images of the cone points with cone angles less than or equal to $\pi$. We show that such maps are homeomorphisms and that they depend smoothly on the target metric. For fixed geometric data, the space of minimizers in relative degree one homotopy classes is a complex manifold of (complex) dimension equal to the number of cone points with cone angles less than or equal to $\pi$. When the genus is zero, we prove the same relative minimization provided there are at least three cone points of cone angle less than or equal to $\pi$.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Gell-Redman, Jesse David |
|---|---|
| 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 | Jesse David Gell-Redman. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2011. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Jesse David Gell-Redman
- License
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
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