Perelman???s Stability Theorem

By V. Kapovitch. 2007

142 citations recorded by the source corpus.

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 .

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/99335577c0c536f4a0f85fee8963d27cdda744f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Luigi Ambrosio
2. A. Lytchak
3. Shouhei Honda
4. Nicola Gigli
5. J. Lott
6. Koichi Nagano
7. Bruce Kleiner
8. David Tewodrose

In Mathematical Physics

1. Koichi Nagano
2. A. Lytchak
3. J. Lott
4. Luigi Ambrosio
5. Bruce Kleiner
6. Shouhei Honda
7. S. Wenger
8. X. Cabré

Citations in the corpus

• Geodesically complete spaces with an upper curvature bound (2018, methodology): “iner (unpublished) and appeared in [Kra11]. The term homotopy equivalent in Theorem 1.12 cannot be replaced by ”homeomorphic” (Example 15.2 below), as it were the case for Alexandrov spaces, [Per91], [Kap07]. This example shows that, for general GCBA spaces, there is no hope of obtaining a local con”
• Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K, N)$-spaces (2017, background): “It is also well known as a direct consequence of Perelman’s stability theorem [44] (see also [34]) that for fixed n ∈ N, K ∈ R and d, v > 0 the isometry class of n-dimensional compact Alexandrov spaces X of sectional curvature bounded below by K with diam X ≤ d and Hn(X) ≥ v has only finitely many t”
• Notes on Perelman's papers (2006, background): “(A proof of Perelman’s stability theorem appears in Kapovitch [34]).”