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Sectional and intermediate Ricci curvature lower bounds via optimal transport
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Ketterer, Christian and Mondino, Andrea (2018) Sectional and intermediate Ricci curvature lower bounds via optimal transport. Advances in Mathematics, 329 . pp. 781-818. doi:10.1016/j.aim.2018.01.024 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2018.01.024
Abstract
The goal of the paper is to give an optimal transport characterization of sectional curvature lower (and upper) bounds for smooth n-dimensional Riemannian manifolds. More generally we characterize, via optimal transport, lower bounds on the so called p-Ricci curvature which corresponds to taking the trace of the Riemann curvature tensor on p -dimensional planes, 1≤p≤n. Such characterization roughly consists on a convexity condition of the p -Renyi entropy along L2-Wasserstein geodesics, where the role of reference measure is played by the p-dimensional Hausdorff measure. As application we establish a new Brunn–Minkowski type inequality involving p-dimensional submanifolds and the p-dimensional Hausdorff measure.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Riemannian manifolds, Ricci flow, Geodesics (Mathematics) | |||||||||
Journal or Publication Title: | Advances in Mathematics | |||||||||
Publisher: | Academic Press | |||||||||
ISSN: | 0001-8708 | |||||||||
Official Date: | 30 April 2018 | |||||||||
Dates: |
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Volume: | 329 | |||||||||
Page Range: | pp. 781-818 | |||||||||
DOI: | 10.1016/j.aim.2018.01.024 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 17 January 2018 | |||||||||
Date of first compliant Open Access: | 6 March 2019 | |||||||||
RIOXX Funder/Project Grant: |
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