Needle Decompositions in Riemannian Geometry

ISBN-13: 9781470425425 / Angielski

Bo'az Klartag

Opis

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.

Spis treści

• Introduction
• Regularity of geodesic foliations
• Conditioning a measure with respect to a geodesic foliation
• The Monge-Kantorovich problem
• Some applications
• Further research
• Appendix: The Feldman-McCann proof of Lemma 2.4.1
• Bibliography.