Communications in Analysis and Geometry

Volume 27 (2019)

Number 2

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

Pages: 491 – 509



Wilderich Tuschmann (Institut für Algebra und Geometrie, Karlsruher Institut für Technologie, Karlsruhe, Germany)

Michael Wiemeler (Mathematisches Institut, Universität Münster, Germany)


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.

Received 1 February 2016

Accepted 25 January 2017

Published 23 August 2019