Compactness of self-shrinkers in $\mathbb R^3$ with fixed genus

Ao Sun; Zhichao Wang

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Compactness of self-shrinkers in $\mathbb R^3$ with fixed genus

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arxiv 1811.05387 v2 pith:DSO5IHGU submitted 2018-11-13 math.DG math.GT

Ao Sun , Zhichao Wang This is my paper · ORCID

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keywords genusboundedcompactnessentropyfixedmathbbself-shrinkerscorollary

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abstract

We prove the compactness of self-shrinkers in $\mathbb R^3$ with bounded entropy and fixed genus. As a corollary, we show that numbers of ends of such surfaces are uniformly bounded by the entropy and genus.

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