Needle Decompositions in Riemannian Geometry
Author | : Bo'az Klartag |
Publisher | : |
Total Pages | : 77 |
Release | : 2017 |
ISBN-10 | : 1470441276 |
ISBN-13 | : 9781470441272 |
Rating | : 4/5 (272 Downloads) |
Download or read book Needle Decompositions in Riemannian Geometry written by Bo'az Klartag and published by . This book was released on 2017 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.