Needle Decompositions in Riemannian Geometry
Author | : Bo’az Klartag |
Publisher | : American Mathematical Soc. |
Total Pages | : 90 |
Release | : 2017-09-25 |
ISBN-10 | : 9781470425425 |
ISBN-13 | : 1470425424 |
Rating | : 4/5 (25 Downloads) |
Download or read book Needle Decompositions in Riemannian Geometry written by Bo’az Klartag and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 90 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, the author's 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 a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.