Perelman's Stability Theorem

Vitali Kapovitch
2006 Surveys in Differential Geometry  
We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence X i of Alexandrov spaces with curv k Gromov-Hausdorff converging to a compact Alexandrov space X , X i is homeomorphic to X for all large i.
doi:10.4310/sdg.2006.v11.n1.a5 fatcat:n7o2bu4fvjb6lk22pu25uiu3py