{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/104584"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/104584","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The Morse index of mean curvature flow self-shrinkers","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.","abstract_html":"In this thesis, we will introduce a notion of index of shrinkers of the mean curvature flow. 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