Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry

DOI10.1007/s11464-020-0824-2OpenAlexW3012444794WikidataQ125313796 ScholiaQ125313796MaRDI QIDQ2184263

Hongzhi Huang

Publication date: 28 May 2020

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.07383

zbMATH Keywords

Ricci curvaturefibrationsbounded Ricci covering geometrynilpotent structuresstability for group actions

Mathematics Subject Classification ID

Rigidity results (53C24) 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)

Related Items (5)

Some topological results of Ricci limit spaces ⋮ A generalized \(\pi_2\)-diffeomorphism finiteness theorem ⋮ Collapsed manifolds with Ricci bounded covering geometry ⋮ Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing ⋮ Ricci flow smoothing for locally collapsing manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Topology and \(\epsilon\)-regularity theorems on collapsed manifolds with Ricci curvature bounds
• Collapsing Riemannian manifolds to ones of lower dimensions
• A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters
• Controlled geometry via smoothing
• The fundamental groups of almost nonnegatively curved manifolds
• Hausdorff perturbations of Ricci-flat manifolds and the splitting theorem
• Ricci curvature and volume convergence
• On the structure of spaces with Ricci curvature bounded below. I
• On the structure of spaces with Ricci curvature bounded below. III
• Shape of manifolds with positive Ricci curvature
• Smoothing Riemannian metrics with Ricci curvature bounds
• Lower bounds on Ricci curvature and the almost rigidity of warped products
• Nonnegative Ricci curvature, stability at infinity and finite generation of fundamental groups
• Quantitative volume space form rigidity under lower Ricci curvature bound. I
• Margulis lemma for compact Lie groups
• How to conjugate C\(^1\)-close group actions
• Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below
• Equivalence of nearby differentiable actions of a compact group
• Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
• Quantitative volume space form rigidity under lower Ricci curvature bound II
• Manifolds of Ricci curvature and local rewinding volume bounded below
• Collapsed manifolds with Ricci bounded covering geometry
• Almost flat manifolds
• Almost flat manifolds

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