Riemann curvature tensor on \(\mathsf{RCD}\) spaces and possible applications

DOI10.1016/j.crma.2019.06.003zbMath1432.53060arXiv1902.02282OpenAlexW2963623267MaRDI QIDQ2324101

Nicola Gigli

Publication date: 13 September 2019

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.02282

zbMATH Keywords

Alexandrov spacesRCD spacesRiemann curvature tensor

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (1)

On the notion of parallel transport on \textsf{RCD} spaces

Cites Work

• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
• Ricci curvature on Alexandrov spaces and rigidity theorems
• Sectional curvature for Riemannian manifolds with density
• Differentiability of Lipschitz functions on metric measure spaces
• On the structure of spaces with Ricci curvature bounded below. I
• Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes
• Recognizing the flat torus among \(\mathsf{RCD}^*(0,N)\) spaces via the study of the first cohomology group
• The weighted connection and sectional curvature for manifolds with density
• Conformal deformations of CAT(0) spaces
• CD meets CAT
• Alexandrov meets Lott--Villani--Sturm
• Riemannian Geometry
• Semiconcave functions in Alexandrov's geometry
• Non-collapsed spaces with Ricci curvature bounded from below
• Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
• Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces

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