| eBook ISBN: | 978-1-4704-4127-2 |
| Product Code: | MEMO/249/1180.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
| eBook ISBN: | 978-1-4704-4127-2 |
| Product Code: | MEMO/249/1180.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 249; 2017; 77 pp
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Regularity of geodesic foliations
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3. Conditioning a measure with respect to a geodesic foliation
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4. The Monge-Kantorovich problem
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5. Some applications
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6. Further research
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Appendix: The Feldman-McCann proof of Lemma 2.4.1
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Additional Material
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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.
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Chapters
-
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
