Regularity of limits of noncollapsing sequences of manifolds

2001/09/11 by Kapovitch, Vitali · 1 citation
#53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.math/0109075

Abstract

We prove that iterated spaces of directions of a limit of a noncollapsing sequence of manifolds with lower curvature bound are topologically spheres. As an application we show that for any finite dimensional Alexandrov space Xⁿ with n≥ 5 there exists an Alexandrov space Y homeomorphic to X which can not be obtained as such a limit.

Cited by

• Minimal Degrees, Volume Growth, and Curvature Decay on Complete Kähler Manifolds

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