| dc.contributor.advisor | Tobias H. Colding. | en_US |
| dc.contributor.author | Liu, Zihan Hans | en_US |
| dc.contributor.other | Massachusetts Institute of Technology. Department of Mathematics. | en_US |
| dc.date.accessioned | 2016-09-30T19:36:54Z | |
| dc.date.available | 2016-09-30T19:36:54Z | |
| dc.date.copyright | 2016 | en_US |
| dc.date.issued | 2016 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1721.1/104584 | |
| dc.description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. | en_US |
| dc.description | Cataloged from PDF version of thesis. | en_US |
| dc.description | Includes bibliographical references (pages 67-69). | en_US |
| dc.description.abstract | In this thesis, we will introduce a notion of index of shrinkers of the mean curvature flow. We will then prove a gap theorem for the index of rotationally symmetric immersed shrinkers in R3, namely, that such shrinkers have index at least 3, unless they are one of the stable ones: the sphere, the cylinder, or the plane. We also provide a generalization of the result to higher dimensions. | en_US |
| dc.description.statementofresponsibility | by Zihan Hans Liu. | en_US |
| dc.format.extent | 69 pages | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | Massachusetts Institute of Technology | en_US |
| dc.rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. | en_US |
| dc.rights.uri | http://dspace.mit.edu/handle/1721.1/7582 | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | The Morse index of mean curvature flow self-shrinkers | en_US |
| dc.type | Thesis | en_US |
| dc.description.degree | Ph. D. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
| dc.identifier.oclc | 958714914 | en_US |
