A warped product version of the Cheeger-Gromoll splitting theorem
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Publication:5267988
DOI10.1090/tran/7003zbMath1368.53031arXiv1506.03800OpenAlexW2963981122WikidataQ125622329 ScholiaQ125622329MaRDI QIDQ5267988
Publication date: 14 June 2017
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.03800
Ricci curvaturewarped productsmooth densityCheeger-Gromoll splitting theoremfundamental group of a compact manifold
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Cites Work
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- An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
- Displacement convexity of generalized relative entropies
- Sectional curvature for Riemannian manifolds with density
- Comparison geometry for the Bakry-Emery Ricci tensor
- Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature
- Convex measures on locally convex spaces
- On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
- On fundamental groups of manifolds of nonnegative curvature
- The weighted connection and sectional curvature for manifolds with density
- Harmonic measures on the sphere via curvature-dimension
- Brascamp-Lieb-type inequalities on weighted Riemannian manifolds with boundary
- Displacement convexity of generalized relative entropies. II
- The splitting theorem for manifolds of nonnegative Ricci curvature
- Variétés kählériennes à première classe de Chern non negative et variétés riemanniennes à courbure de Ricci généralisée non negative. (Kählerian manifolds of non-negative first Chern class and Riemannian manifolds with non-negative generalized Ricci curvature)
- \((K,N)\)-convexity and the curvature-dimension condition for negative \(N\)
- Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
- Beyond traditional Curvature-Dimension I: New model spaces for isoperimetric and concentration inequalities in negative dimension
- Book Review: Geometry of isotropic convex bodies
- Positive weighted sectional curvature
- A curvature condition for a twisted product to be a warped product