On the finiteness of the Morse index of self-shrinkers

Xu-Yong Jiang; He-Jun Sun; Peibiao Zhao

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arXiv · 2106.12415

On the finiteness of the Morse index of self-shrinkers

Xu-Yong Jiang·He-Jun Sun·Peibiao Zhao

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Abstract

In this paper, we present a sufficient condition for finite Morse index of complete properly self-shrinkers. We prove that a complete properly embedded self-shrinker in $\mathbb{R}^{n+1}$ with finite asymptotically conical ends or asymptotically cylindrical ends must have finite Morse index. Moreover, as an application of this result, we show that a complete properly embedded self-shrinker in $\mathbb{R}^3$ with finite genus has finite Morse index.

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Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao. 2021-06-23. On the finiteness of the Morse index of self-shrinkers. https://arxiv.org/abs/2106.12415

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