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arXiv · 1908.06146

The Heintze-Karcher inequality for metric measure spaces

Christian Ketterer
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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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Christian Ketterer. 2019-08-16. The Heintze-Karcher inequality for metric measure spaces. https://arxiv.org/abs/1908.06146

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