Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces
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Publication:974040
DOI10.4007/annals.2010.171.343zbMath1192.53040arXivmath/0506273OpenAlexW3101340897WikidataQ125564885 ScholiaQ125564885MaRDI QIDQ974040
Vitali Kapovitch, Wilderich Tuschmann, Anton Petrunin
Publication date: 27 May 2010
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0506273
Related Items (28)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Volume and bounded cohomology
- Curvature, diameter and Betti numbers
- Collapsing and pinching under a lower curvature bound
- The fundamental groups of almost nonnegatively curved manifolds
- Hausdorff perturbations of Ricci-flat manifolds and the splitting theorem
- Infinitesimal computations in topology
- The Pogorelov-Klingenberg theorem for manifolds homeomorphic to \(\mathbb R^n\)
- Parallel transportation for Alexandrov space with curvature bounded below
- On fundamental groups of manifolds of nonnegative curvature
- Contributions of rational homotopy theory to global problems in geometry
- Metrics of positive Ricci curvature on quotient spaces
- On the fundamental groups of manifolds of positive sectional curvature
- Variations on a theme of Minkowski and Serre
- The almost cyclicity of the fundamental groups of positively curved manifolds
- Zero entropy and bounded topology
- Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds
- Semiconcave functions in Alexandrov's geometry
- Open map theorem for metric spaces
- Gradient flows on Wasserstein spaces over compact Alexandrov spaces
- Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
- Almost flat manifolds
- Symplectic manifolds with no Kähler structure
- Ricci curvature, minimal volumes, and Seiberg-Witten theory
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