Santiago Cordero-Misteli, Giada Franz
Published 2022-06-05Version 1
Given a compact Riemannian manifold with boundary of dimension between 3 and 7, we show that the Morse index of a free boundary minimal hypersurface grows linearly with the sum of its Betti numbers, where the constant of growth depends on the area of the free boundary minimal hypersurface in question. We are inspired by a groundbreaking combinatorial argument by Song (2019), which we partly simplify and shorten.
Comments: 21 pages, 3 figures
Betti and Tachibana numbers
Gradient estimate for the Poisson equation and the non-homogeneous heat equation on compact Riemannian manifolds
Critical functions and elliptic PDE on compact riemannian manifolds
![QR code for arXiv:2206.02105 [math.DG]](http://oss.arxitics.com/images/favicon.svg)