Differentiable stability and sphere theorems for manifolds and Einstein manifolds with positive scalar curvature

Abstract

Leon Green obtained remarkable rigidity results for manifolds of positive scalar curvature with large conjugate radius and/or injectivity radius. Using $C^{k,\alpha }$ convergence techniques, we prove several differentiable stability and sphere theorem versions of these results and apply those also to the study of Einstein manifolds.

13 pages; final version; accepted for publication in Comm. Anal. Geom

References in corpus (2)

• Einstein manifolds with nonnegative isotropic curvature are locally symmetric
• Intrinsic flat convergence with bounded Ricci curvature