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On the free boundary min-max geodesics

Xin Zhou Massachusetts Institute of Technology

Differential Geometry mathscidoc:1610.10032

International Mathematics Research Notices, 5, 1447-1466, 2016
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.
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@inproceedings{xin2016on,
  title={On the free boundary min-max geodesics},
  author={Xin Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010161839465364111},
  booktitle={International Mathematics Research Notices},
  volume={5},
  pages={1447-1466},
  year={2016},
}
Xin Zhou. On the free boundary min-max geodesics. 2016. Vol. 5. In International Mathematics Research Notices. pp.1447-1466. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010161839465364111.
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