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DOI: https://doi.org/10.1007/s11464-010-0079-4

RESEARCH ARTICLE

A quadrangle comparison theorem and its application to soul theory for Alexandrov spaces

  • Jianguo CAO 1,2 ,
  • Bo DAI , 3 ,
  • Jiaqiang MEI 2,4
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  • 1. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA
  • 2. Department of Mathematics, Nanjing University, Nanjing 210093, China
  • 3. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 4. Institute of Mathematical Science, Nanjing University, Nanjing 210093, China

Received date: 03 Mar 2010

Accepted date: 20 Jun 2010

Published date: 01 Feb 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We shall derive two sufficient conditions for complete finitedimensional Alexandrov spaces of nonnegative curvature to be contractible. One of the new technical tools used in our proof is a quadrangle comparison theorem inspired by Perelman.

Key words： Alexandrov space with nonnegative curvature; soul theory; quadrangle comparison theorem

Cite this article

Jianguo CAO , Bo DAI , Jiaqiang MEI . A quadrangle comparison theorem and its application to soul theory for Alexandrov spaces[J]. Frontiers of Mathematics in China, 0 , 6(1) : 35 -48 . DOI: 10.1007/s11464-010-0079-4

References

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