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

Tuschmann W.; Wiemeler M.

Abstract

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