Lower bounds for the index of compact constant mean curvature surfaces in \mathbb R³ and \mathbb S³

2017/11/20 by Cavalcante, Marcos P., de Oliveira, Darlan F.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.07233

Abstract

Let M be a compact constant mean curvature surface either in \mathbbS³ or ℝ³. In this paper we prove that the stability index of M is bounded 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.

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