Perelman's Stability Theorem

Vitali Kapovitch

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Perelman's Stability Theorem

Vitali Kapovitch

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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 $i$.

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Vitali Kapovitch. 2007-03-13. Perelman's Stability Theorem. https://arxiv.org/abs/math/0703002

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