Lower bounds for the index of compact constant mean curvature surfaces in ${\mathbb{R}}^3$ and ${\mathbb{S}}^3$

Marcos P. Cavalcante, Darlan F. de Oliveira

Let $M$ be a compact constant mean curvature surface either in ${\mathbb{S}}^3$ or ${\mathbb{R}}^3$. In this paper we prove that the stability index of $M$ is bounded below by a linear…