Perelman's Stability Theorem

Abstract

We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with curvature bounded below Gromov-Hausdorff converging to a compact Alexandrov space $X$, $X_i$ is homeomorphic to $X$ for all large $i$.

revised introduction

Cited by in corpus (2)

• Completion of the Proof of the Geometrization Conjecture
• Weak collapsing and geometrisation of aspherical 3-manifolds