Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature |
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| Authors: | Qintao Deng Fernando Galaz-García Luis Guijarro Michael Munn |
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| Institution: | 1.School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan,People’s Republic of China;2.Karlsruher Institut für Technologie (KIT),Institut für Algebra und Geometrie,Karlsruhe,Germany;3.Department of Mathematics,Universidad Autónoma de Madrid,Madrid,Spain;4.ICMAT CSIC-UAM-UCM-UC3M,Madrid,Spain;5.Courant Institute,New York University,New York,USA |
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| Abstract: | We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the CD ?(K,N) sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we show that a closed three-dimensional CD ?(2,3)-Alexandrov space must be homeomorphic to a spherical space form or to the suspension of \(\mathbb {R}P^{2}\). We then classify closed three-dimensional CD ?(0,3)-Alexandrov spaces. |
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