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

Published 13 Nov 2018 in math.DG and math.GT | (1811.05387v2)

Abstract: We prove the compactness of self-shrinkers in $\mathbb R3$ 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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