The Heintze-Karcher inequality for metric measure spaces

2019/08/16 by Ketterer, Christian · 2 citations
#30L99 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1908.06146

Abstract

In this note we prove the Heintze-Karcher inequality in the context of essentially non-branching metric measure spaces satisfying a lower Ricci curvature bound in the sense of Lott-Sturm-Villani. The proof is based on the the needle decomposition technique for metric measure spaces introduced by Cavalletti-Mondino. Moreover, in the class of spaces satisfying a Riemannian curvature-dimension condition with positive curvature the equality case is characterized.

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• Variational properties of the total inverse mean curvature in the plane under boundary constraints
• Mean curvature and sharp Willmore inequalities in metric spaces

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