Index Characterization for Free Boundary Minimal Surfaces
Differential Geometry
2020-06-26 v4
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.
Cite
@article{arxiv.1609.01651,
title = {Index Characterization for Free Boundary Minimal Surfaces},
author = {Hung Tran},
journal= {arXiv preprint arXiv:1609.01651},
year = {2020}
}
Comments
fixed several typos regarding the nullity and others