Bounds on the Volume Entropy and Simplicial Volume in Ricci Curvature Lp-Bounded from Below

DOI10.1093/IMRN/RNP006zbMath1182.53034arXiv0810.0149OpenAlexW1989154613MaRDI QIDQ3633177

Erwann Aubry

Publication date: 17 June 2009

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.0149

zbMATH Keywords

least eigenvalueRiemannian coverRicci curvature \(L^p\)-bounded from belowvolume entropy, Gromov-Hausdorff distance

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Manifolds of metrics (especially Riemannian) (58D17)

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Geometric and spectral estimates based on spectral Ricci curvature assumptions ⋮ Gradient estimates of positive solutions for the weighted nonlinear parabolic equation ⋮ Comparison geometry for integral radial Bakry-Émery Ricci tensor bounds ⋮ Quantitative rigidity of almost maximal volume entropy for both \(\mathsf{RCD}^\ast\) spaces and integral Ricci curvature bound ⋮ Comparison geometry for integral Bakry-Émery Ricci tensor bounds ⋮ Euclidean volume growth for complete Riemannian manifolds ⋮ Myers' type theorem for integral Bakry-Émery Ricci tensor bounds ⋮ Local Sobolev constant estimate for integral Bakry-Émery Ricci curvature ⋮ Improved relative volume comparison for integral Ricci curvature and applications to volume entropy

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