On the finiteness of the Morse index of self-shrinkers

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.

13 pages

References in corpus (1)

• Asymptotic structure of self-shrinkers