Sphere Theorems with and without Smoothing

Abstract

We show two sphere theorems for the Riemannian manifolds with scalar curvature bounded below and the non-collapsed $\mathrm{RCD}(n-1,n)$ spaces with mean distance close to $\frac{\pi }{2}$.

Appeared in Journal of Geometry

References in corpus (4)

• Optimal maps in essentially non-branching spaces
• Sphere Theorems in Geometry
• Curvature-Dimension Condition Meets Gromov's $n$-Volumic Scalar Curvature
• Enlargeable Length-structures and Scalar Curvatures