Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds

Abstract

In this short note we review some known results on the structure and regularity of spaces with lower Ricci curvature bounds. We present some known and new open questions about next steps.

arXiv commentv2: Corollary 2.20 corrected

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• Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below
• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II
• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below

Cited by in corpus (5)

• Examples of Ricci limit spaces with non-integer Hausdorff dimension
• The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth
• On manifolds with almost non-negative Ricci curvature and integrally-positive $k^{th}$-scalar curvature
• A lower bound for the curvature integral under an upper curvature bound
• Rectifiability; a survey