Needle Decompositions in Riemannian Geometry

Ebook Details

Authors

Bo'az Klartag

Year 2017
Pages 77
Publisher Amer Mathematical Society
Language en
ISBN 9781470425425
File Size 717.79 KB
File Format PDF
Download Counter 99
Amazon Link

Ebook Description

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.