Perelman’s Stability Theorem

2006/01/01 by Vitali Kapovitch · 4 citations
Mathematics · #Advanced Operator Algebra Research #Computer science #Economics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical economics #Mathematics #Stability (learning theory)

paper · doi:10.4310/sdg.2006.v11.n1.a5

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

Abstract. We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence Xi of Alexandrov spaces with curv � k Gromov-Hausdorff converging to a compact Alexandrov space X, Xi is homeomorphic to X for all large i. 1.

Citations

• Approximating Homotopy Equivalences by Homeomorphisms
• Volume collapsed three-manifolds with a lower curvature bound
• The topology of four-dimensional manifolds

Cited by

• Quantitative bi-Lipschitz embeddings of bounded-curvature manifolds and orbifolds
• Orbifold homeomorphism finiteness based on geometric constraints
• A knot characterization and 1–connected nonnegatively curved 4–manifolds with circle symmetry
• Grigori Perelman [wikipedia]