Needle decompositions in Riemannian geometry

Bo'az Klartag

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arXiv · 1408.6322

Needle decompositions in Riemannian geometry

Bo'az Klartag

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Abstract

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to an integrable geodesic foliation. The Monge mass transfer problem plays an important role in our analysis.

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Bo'az Klartag. 2014-08-27. Needle decompositions in Riemannian geometry. https://arxiv.org/abs/1408.6322

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