The Morse index of mean curvature flow self-shrinkers

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2016

Author dc:creator

• Liu, Zihan Hans

Advisor dc:contributor.advisor

• Tobias H. Colding.

• Mathematics.

Statement 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/104584

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/104584