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

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.

Keywords

Alexandrov space with nonnegative curvature / soul theory / quadrangle comparison theorem

References

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