The Heintze-Karcher inequality, a Riemannian volume comparison theorem, is generalized to essentially non-branching metric measure spaces with lower Ricci curvature bounds, with a rigidity result for RCD spaces.
Caffarelli, Mikhail Feldman, and Robert J
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The Heintze-Karcher inequality for metric measure spaces
The Heintze-Karcher inequality, a Riemannian volume comparison theorem, is generalized to essentially non-branching metric measure spaces with lower Ricci curvature bounds, with a rigidity result for RCD spaces.