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

Abstract

We shall derive two sufficient conditions for complete finite-dimensional 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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