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Index Characterization for Free Boundary Minimal Surfaces (1609.01651v4)

Published 6 Sep 2016 in math.DG

Abstract: In this paper, we compute the Morse index for a free boundary minimal submanifold from data of two simpler problems. The first one is the corresponding problem with fixed boundary condition; and the second is associated with the Dirichlet-to-Neumann map for Jacobi fields. 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.