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Needle Decompositions in Riemannian Geometry.


Needle Decompositions in Riemannian Geometry

Bo'az Klartag

American Mathematical Society


77 pages


Memoirs of the American Mathematical Society; Volume 249, Number 1180


When the Ricci curvature is non-negative, says Klartag, log-concave measure are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level of sets of a Lipschitz function. Based on that observation, he generalizes the localization technique from convex geometry to the setting of Riemannian manifolds with Ricci curvature that is bounded from below. The Monge mass transfer problem plays an important role in his analysis. ([umlaut] Ringgold, Inc., Portland, OR)

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Title Annotation:Bo'az Klartag
Article Type:Book review
Date:Oct 1, 2017
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