JournalsrmiVol. 36, No. 1pp. 195–206

Lower bounds for the index of compact constant mean curvature surfaces in R3\mathbb R^3 and S3\mathbb S^3

  • Marcos Petrúcio Cavalcante

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

    Universidade Estadual de Feira de Santana, Brazil
Lower bounds for the index of compact constant mean curvature surfaces in $\mathbb R^3$ and $\mathbb S^3$ cover

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Abstract

Let MM be a compact constant mean curvature surface either in S3\mathbb S^3 or R3\mathbb R^3. In this paper we prove that the stability index of MM 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 MM and those of Hodge Laplacian of 1-forms on MM.

Cite this article

Marcos Petrúcio Cavalcante, Darlan Ferreira de Oliveira, Lower bounds for the index of compact constant mean curvature surfaces in R3\mathbb R^3 and S3\mathbb S^3. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 195–206

DOI 10.4171/RMI/1125