Mathematical analysis

Pure mathematics

Mathematics

Riemannian geometry

Geometry

Memoirs of the American Mathematical Society

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. 2010 Mathematics Subject Classification. 53C21, 52A20, 52A40 .

Needle Decompositions in Riemannian Geometry