Needle Decompositions in Riemannian Geometry
Author | : Bo'az Klartag |
Publisher | : |
Total Pages | : 77 |
Release | : 2017 |
Genre | : Curvature |
ISBN | : 9781470441272 |
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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 nonnegative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in our analysis.