A Canonical Proof of Perelman's Stability Theorem
数学专题报告
报告题目(Title)：A Canonical Proof of Perelman's Stability Theorem
报告人(Speaker)：李楠 教授（美国纽约城市大学）
地点(Place)：后主楼1223
时间(Time)：2026年4月28日（周二）15:30-16:30
邀请人(Inviter)：葛剑
报告摘要
Perelman's remarkable stability theorem states that if X is a compact n-dimensional Alexandrov space with curvature ≥ k, then for any ε > 0, there exists δ = δ (X, ε) > 0 such that for any n-dimensional Alexandrov space Y with curvature ≥ k, if Y is Gromov-Hausdorff close to X by a δ-approximation f: X → Y, then there is a homeomorphism g: X → Y which is ε-close to f. We present a canonical proof of this theorem, for which the homeomorphism f is constructed purely in line with the metrics of X and Y.
