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

TL;DR

This paper reviews known results and open questions concerning the structure and regularity of spaces with lower Ricci curvature bounds, highlighting areas for future research.

Contribution

It provides a summary of existing knowledge and introduces new open questions about the geometric and regularity properties of Ricci curvature bounded spaces.

Findings

Summary of known results on Ricci curvature spaces

Presentation of new open questions for future research

Discussion of potential directions for advancing understanding

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.