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

Zhichao Wang; Bo Zhu

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arXiv · 2109.12715

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

Zhichao Wang·Bo Zhu

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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.

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Zhichao Wang, Bo Zhu. 2021-09-26. Uryson width of three dimensional mean convex domain with non-negative Ricci curvature. https://arxiv.org/abs/2109.12715

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