Stability of almost submetries

DOI10.1007/s11464-010-0076-7zbMath1213.53050OpenAlexW2036159796MaRDI QIDQ2430826

Shicheng Xu, Xiaochun Rong

Publication date: 8 April 2011

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

Full work available at URL: https://doi.org/10.1007/s11464-010-0076-7

zbMATH Keywords

stabilityAlexandrov spacefibre bundleGromov-Hausdorff convergence(almost) submetry

Mathematics Subject Classification ID

Metric geometry (51F99) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Fiber bundles in algebraic topology (55R10) Deformations of fiber bundles (32G08)

Related Items (3)

Pointed Gromov-Hausdorff topological stability for non-compact metric spaces ⋮ A parametrized compactness theorem under bounded Ricci curvature ⋮ Stability of \(e^\epsilon\)-Lipschitz and co-Lipschitz maps in Gromov-Hausdorff topology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lipschitz convergence of Riemannian manifolds
• Collapsing and pinching under a lower curvature bound
• A radius sphere theorem
• A metric characterization of Riemannian submersions
• Finiteness theorems for submersions and souls
• Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.
• Semiconcave functions in Alexandrov's geometry
• Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
• A.D. Alexandrov spaces with curvature bounded below
• A finiteness theorem for Riemannian submersions
• Bounded Riemannian submersions
• A parametrized geometric finitness theorem
• Finiteness Theorems for Riemannian Manifolds

This page was built for publication: Stability of almost submetries