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

### Marcos Petrúcio Cavalcante

Universidade Federal de Alagoas, Maceió, Brazil### Darlan Ferreira de Oliveira

Universidade Estadual de Feira de Santana, Brazil

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## Abstract

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 from below by a linear function of the genus. As a by-product we obtain a comparison theorem between the spectrum of the Jacobi operator of $M$ and those of Hodge Laplacian of 1-forms on $M$.

## Cite this article

Marcos Petrúcio Cavalcante, Darlan Ferreira de Oliveira, Lower bounds for the index of compact constant mean curvature surfaces in $\mathbb R^3$ and $\mathbb S^3$. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 195–206

DOI 10.4171/RMI/1125