The Morse index of mean curvature flow self-shrinkers

Author(s)
Liu, Zihan Hans
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Tobias H. Colding.
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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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 67-69).
 
Date issued
2016
URI
http://hdl.handle.net/1721.1/104584
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.
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