The Brunn-Minkowski inequality implies the CD condition in weighted Riemannian manifolds

DOI10.1016/j.na.2024.113502arXiv2209.13424OpenAlexW4297949652WikidataQ128525591 ScholiaQ128525591MaRDI QIDQ6154889

Lorenzo Portinale, Tommaso Rossi, Mattia Magnabosco

Publication date: 12 March 2024

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.13424

zbMATH Keywords

Ricci curvatureBrunn-Minkowski inequalitycurvature-dimension bounds

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Local Riemannian geometry (53B20)

Cites Work

• Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
• On the regularity of solutions of optimal transportation problems
• On Borell-Brascamp-Lieb inequalities on metric measure spaces
• Finsler interpolation inequalities
• A convexity principle for interacting gases
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• Sub-Riemannian interpolation inequalities
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequalities
• The globalization theorem for the curvature-dimension condition
• Ricci curvature for metric-measure spaces via optimal transport
• On the measure contraction property of metric measure spaces
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group
• The Brunn-Minkowski inequality
• Optimal Transport
• Polar factorization of maps on Riemannian manifolds