Communications in Analysis and Geometry
Volume 28 (2020)
Index characterization for free boundary minimal surfaces
Pages: 189 – 222
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.
Received 13 September 2016
Accepted 4 July 2017
Published 12 March 2020