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Needle decompositions in Riemannian geometry / Bo'az Klartag.

By: Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 249, no 1180.Publication details: Providence : American Mathematical Society, 2017.Description: v, 77 pages ; 26 cmISBN:
  • 9781470425425 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Regularity of geodesic foliations -- 3. Conditioning a measure with respect to a geodesic foliation -- 4. The Monge-Kantorovich problem -- 5. Some applications -- 6. Further research -- Appendix: The Feldman-McCann proof of Lemma 2.4.1 Bibliography.
Summary: 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.
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Includes bibliographical references.

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

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.

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