Soul theorem for 4-dimensional topologically regular open nonnegatively curved Alexandrov spaces

DOI10.1090/S0002-9939-2011-10831-1zbMath1244.53081arXiv1010.1863OpenAlexW2963462534MaRDI QIDQ3104464

Jian Ge

Publication date: 13 December 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.1863

zbMATH Keywords

soul theoremAlexandrov spaces

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Synthetic differential geometry (51K10)

Cites Work

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• Collapsing three-manifolds under a lower curvature bound.
• On complete open manifolds of positive curvature
• On the structure of complete manifolds of nonnegative curvature
• Semiconcave functions in Alexandrov's geometry
• An optimal extension of Perelman's comparison theorem for quadrangles and its applications

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