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 $i$.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2007
- DOI:
- 10.48550/arXiv.math/0703002
- arXiv:
- arXiv:math/0703002
- Bibcode:
- 2007math......3002K
- Keywords:
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- Mathematics - Differential Geometry;
- 53C20
- E-Print:
- revised introduction