Needle decompositions in Riemannian geometry
著者
書誌事項
Needle decompositions in Riemannian geometry
（Memoirs of the American Mathematical Society, no. 1180）
American Mathematical Society, 2017
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注記
"Volume 249, number 1180 (first of 8 numbers), September 2017"
Bibliography: p. 75-77
内容説明・目次
内容説明
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.
目次
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.
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