Conjectures and open questions on the structure and regularity of spaces with lower Ricci curvature bounds

DOI10.3842/SIGMA.2020.104zbMath1456.53005arXiv2010.10031OpenAlexW3093959533MaRDI QIDQ2223040

Aaron Naber

Publication date: 28 January 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.10031

zbMATH Keywords

regularityRicci curvatureHausdorff dimensionnoncollapsed spaces

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) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Related Items (5)

Cohn-Vossen inequality on certain noncompact Kähler manifolds ⋮ Examples of Ricci limit spaces with non-integer Hausdorff dimension ⋮ Volume growth of 3-manifolds with scalar curvature lower bounds ⋮ On the spaces with Ricci curvature bounds ⋮ Geometry of positive scalar curvature on complete manifold

Cites Work

• Characterization of tangent cones of noncollapsed limits with lower Ricci bounds and applications
• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
• Quantitative estimates on the singular sets of Alexandrov spaces
• On the structure of spaces with Ricci curvature bounded below. I
• Lower bounds on Ricci curvature and the almost rigidity of warped products
• Lower bounds on Ricci curvature and quantitative behavior of singular sets
• \(L^2\) curvature bounds on manifolds with bounded Ricci curvature
• Lower Ricci curvature, branching and the bilipschitz structure of uniform Reifenberg spaces
• Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below
• <scp>Gromov‐Hausdorff</scp> Limits of Kähler Manifolds with Ricci Curvature Bounded Below <scp>II</scp>

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