English

On the free boundary min-max geodesics

Differential Geometry 2015-04-07 v1

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.

Keywords

Cite

@article{arxiv.1504.00971,
  title  = {On the free boundary min-max geodesics},
  author = {Xin Zhou},
  journal= {arXiv preprint arXiv:1504.00971},
  year   = {2015}
}

Comments

16 pages

R2 v1 2026-06-22T09:09:54.750Z