Resumen de Lower bounds for the index of compact constant mean curvature surfaces in R3 and S3

Marcos Petrúcio Cavalcante, Darlan Ferreira de Oliveira

• Let M be a compact constant mean curvature surface either in S3 or R3. 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.