Ricci Bounds for Euclidean and Spherical Cones

DOI10.1007/978-3-319-00786-1_1zbMath1328.53050arXiv1003.2114OpenAlexW1673989787MaRDI QIDQ2950218

Karl-Theodor Sturm, Kathrin Bacher

Publication date: 8 October 2015

Published in: Singular Phenomena and Scaling in Mathematical Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.2114

zbMATH Keywords

Alexandrov spacescurvature-dimension conditioncomplete Riemannian manifolds

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Cites Work

• Unnamed Item
• Unnamed Item
• Localization and tensorization properties of the curvature-dimension condition for metric measure spaces. II
• Spectral geometry of singular Riemannian spaces
• Isoperimetric regions in spherical cones and Yamabe constants of \(M \times S^{1}\)
• Weak curvature conditions and functional inequalities
• Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
• On the structure of spaces with Ricci curvature bounded below. I
• 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
• On the diffraction of waves by conical singularities. I
• Products, cones, and suspensions of spaces with the measure contraction property
• Optimal Transport