Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
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Publication:3993802
DOI10.2307/2152771zbMath0758.53022OpenAlexW4237886479MaRDI QIDQ3993802
Kenji Fukaya, Jeff Cheeger, Mikhael Gromov
Publication date: 13 August 1992
Full work available at URL: https://doi.org/10.2307/2152771
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Smoothing Riemannian metrics
- Collapsing Riemannian manifolds while keeping their curvature bounded. II
- Geometric construction of holonomy coverings for almost flat manifolds
- Collapsing Riemannian manifolds to ones with lower dimension. II
- Collapsing Riemannian manifolds to ones of lower dimensions
- Collapsing Riemannian manifolds while keeping their curvature bounded. I
- Real analyticity of solutions of Hamilton's equation
- Lipschitz convergence of Riemannian manifolds
- A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters
- Deforming the metric on complete Riemannian manifolds
- Almost nonpositively curved manifolds
- Collapsing and pinching under a lower curvature bound
- Bounds on the von Neumann dimension of \(L^ 2\)-cohomoloy and the Gauss- Bonnet theorem for open manifolds
- How to conjugate C\(^1\)-close group actions
- Almost Lie groups of type n.
- Riemannian center of mass and mollifier smoothing
- Finiteness Theorems for Riemannian Manifolds
- Almost flat manifolds
- Almost flat manifolds
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