Needle decompositions in Riemannian geometry

2014/08/27 by Klartag, Bo'az · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1408.6322

Abstract

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our 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 an integrable geodesic foliation. The Monge mass transfer problem plays an important role in our analysis.

Cited by

• Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization
• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound

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