Communications in Analysis and Geometry

Volume 28 (2020)

Number 1

Index characterization for free boundary minimal surfaces

Pages: 189 – 222

DOI: https://dx.doi.org/10.4310/CAG.2020.v28.n1.a6

Author

Hung Tran (Department of Mathematics, University of California at Irvine)

Abstract

In this paper, we compute the Morse index of a free boundary minimal submanifold from data of two simpler problems. The first is the fixed boundary problem and the second is concered with the Dirichlet-to-Neumann map associated with the Jacobi operator. As an application, we show that the Morse index of a free boundary minimal annulus is equal to $4$ if and only if it is the critical catenoid.

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Received 13 September 2016

Accepted 4 July 2017

Published 12 March 2020