Rigidity and gap results for low index properly immersed self--shrinkers in ${\mathbb{R}}^{m+1}$

Debora Impera

In this paper we show that the only properly immersed self--shrinkers $\Sigma$ in ${\mathbb{R}}^{m+1}$ with Morse index $1$ are the hyperplanes through the origin. Moreover, we prove that…