A sharp comparison theorem for compact manifolds with mean convex boundary

Martin Man-chun Li Chinese University of Hong Kong

Differential Geometry mathscidoc:1910.43014

The Journal of Geometric Analysis, 24, (3), 1490-1496, 2014.7
Let M be a compact n-dimensional Riemannian manifold with nonnegative Ricci curvature and mean convex boundary ∂M. Assume that the mean curvature H of the boundary ∂M satisfies H≥(n−1)k>0 for some positive constant k. In this paper, we prove that the distance function d to the boundary ∂M is bounded from above by 1/𝑘 and the upper bound is achieved if and only if M is isometric to an n-dimensional Euclidean ball of radius 1/𝑘.
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@inproceedings{martin2014a,
  title={A sharp comparison theorem for compact manifolds with mean convex boundary},
  author={Martin Man-chun Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020105709533456543},
  booktitle={The Journal of Geometric Analysis},
  volume={24},
  number={3},
  pages={1490-1496},
  year={2014},
}
Martin Man-chun Li. A sharp comparison theorem for compact manifolds with mean convex boundary. 2014. Vol. 24. In The Journal of Geometric Analysis. pp.1490-1496. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020105709533456543.
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