Inscribed radius bounds for metric measure spaces with mean-H-convex boundary
Christian Ketterer (University of Toronto)
Abstract: We introduce a synthetic lower mean curvature bound for the topological boundary of a subset in a metric measure space that satisfies a lower Ricci curvature bound in the sense of Lott, Sturm and Villani. This lower mean curvature bound coincides with the classical notion in smooth context. As application I present a theorem about sharp comparison estimates for the inscribed radius of such subsets. Moreover, in the context of RCD(0,N) metric measure spaces (Riemannian curvature-dimension condition) equality holds if and only if the subset is isometric to a geodesic ball centered at the tip of an Euclidean cone. This generalizes theorems in smooth context by Kasue and Sakurai to a singular framework. This is a joint work with Annegret Burtscher, Robert McCann and Eric Woolgar.
mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control
Audience: researchers in the topic
Online Seminar "Geometric Analysis"
Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.
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Organizers: | Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang |
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