Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds

DOI10.2140/gt.2017.21.603zbMath1357.49028arXiv1505.02061OpenAlexW1524567323MaRDI QIDQ511621

Andrea Mondino, Fabio Cavalletti

Publication date: 22 February 2017

Published in: Advances in Mathematics, Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.02061

zbMATH Keywords

Heisenberg groupRicci curvaturespectral gapHausdorff measureAlexandrov spaceSobolev inequalitylog-Sobolev inequalitymeasure contraction propertyoptimal transportBrunn-Minkowski inequalitymetric measure spacesTalagrand inequalityRicci curvature lower boundsdisintegration theoremreference measure

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonsmooth analysis (49J52) Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Spaces of measures, convergence of measures (28A33) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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