The Heintze-Karcher inequality for metric measure spaces

Ketterer, Christian

doi:10.1090/proc/15041

The Heintze-Karcher inequality for metric measure spaces
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Proc. Amer. Math. Soc. 148 (2020), 4041-4056 Request permission

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 needle decomposition technique for metric measure spaces introduced by Cavalletti-Mondino. Moreover, in the class of $RCD$ spaces with positive curvature the equality case is characterized.

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