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 the 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.
|Pages (from-to)||24 pages|
|Journal||Communications in Analysis and Geometry|
|State||Published - Jan 2020|