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Let be a compact constant mean curvature surface either in or . In this paper we prove that the stability index of 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 and those of Hodge Laplacian of 1-forms on .
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Marcos Petrúcio Cavalcante, Darlan Ferreira de Oliveira, Lower bounds for the index of compact constant mean curvature surfaces in and . Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 195–206DOI 10.4171/RMI/1125