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arXiv · 1803.09852

Index Estimate of Self-Shrinkers in $\mathbb{R}^3$ with Asymptotically Conical Ends

Nicolau Sarquis Aiex
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Abstract

We construct Gaussian Harmonic forms of finite Gaussian weighted $L^2$-norm on non-compact surfaces that detect each asymptotically conical end. As an application we prove an extension of the index estimates of self-shrinkers in $[11]$ under the existence of such ends. We show that the Morse index of a self-shrinker is greater or equal to $\frac{2g+r-1}{3}$, where $r$ is the number of asymptotically conical ends.

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Nicolau Sarquis Aiex. 2018-03-27. Index Estimate of Self-Shrinkers in $\mathbb{R}^3$ with Asymptotically Conical Ends. https://arxiv.org/abs/1803.09852

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