On the free boundary min-max geodesics

2015/04/04 by Zhou, Xin · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.00971

Abstract

Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational problem. In particular, we develop a modified Birkhoff curve shortening process to achieve a strong "Colding-Minicozzi" type min-max approximation result.

Cited by

• Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds
• Min-max theory and minimal surfaces with prescribed genus

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