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Uryson width of three dimensional mean convex domain with non-negative Ricci curvature
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math.DGmath.GTmath.MG
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boundcurvaturemeanthreeboundaryconvexdimensionalricci
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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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