English

Uryson width of three dimensional mean convex domain with non-negative Ricci curvature

Differential Geometry 2021-09-28 v1 Geometric Topology Metric Geometry

Abstract

We prove that for every three dimensional manifold with nonnegative Ricci curvature and strictly mean convex boundary, there exists a Morse function so that each connected component of its level sets has a uniform diameter bound, which depends only on the lower bound of mean curvature. This gives an upper bound of Uryson 1-width for those three manifolds with boundary.

Keywords

Cite

@article{arxiv.2109.12715,
  title  = {Uryson width of three dimensional mean convex domain with non-negative Ricci curvature},
  author = {Zhichao Wang and Bo Zhu},
  journal= {arXiv preprint arXiv:2109.12715},
  year   = {2021}
}

Comments

18 pages; comments are welcome!