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.

v2: Corollary 2.20 corrected

References in corpus (1)

• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II

Cited by in corpus (4)

• 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