Needle Decompositions in Riemannian Geometry

作者：Klartag Bo'az^*

来源：Memoirs of the American Mathematical Society, 2017, 249(1180): I-77.

DOI：10.1090/memo/1180

• Ricci curvature
• Monge-Kantorovich problem
• needle decomposition
• Riemannian geometry

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.

• 出版日期2017-9