Vol. 305, No. 1, 2020

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Index estimates for free boundary constant mean curvature surfaces

Marcos P. Cavalcante and Darlan F. de Oliveira

Vol. 305 (2020), No. 1, 153–163
Abstract

We consider compact constant mean curvature surfaces with boundary immersed in a mean convex region of the Euclidean space or in the unit sphere. We prove that the weak Morse index is bounded from below by a linear function of the genus and number of boundary components.

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Keywords
constant mean curvature surfaces, Morse index, free boundary surfaces
Mathematical Subject Classification 2010
Primary: 35P15, 49Q10, 53A10
Milestones
Received: 25 March 2018
Revised: 25 March 2019
Accepted: 29 October 2019
Published: 17 March 2020
Authors
Marcos P. Cavalcante
Universidade Federal de Alagoas
Maceió, AL
Brazil
Darlan F. de Oliveira
Universidade Estadual de Feira de Santana
Feira de Santanta, BA
Brazil