On the finiteness of the Morse index of self-shrinkers

2021/06/23 by Xu-Yong Jiang, Xuyong Jiang, Jiang, Xu-Yong +5
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #msc:53C21 #msc:53C24 #msc:53C42

paper · pdf · doi:10.48550/arxiv.2106.12415

13 pages

arxiv created 2021/06/23 · arxiv updated 2021/06/24

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 ℝⁿ⁺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 ℝ³ with finite genus has finite Morse index.

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