Open Alexandrov spaces of nonnegative curvature

Abstract

Let $X$ be an open (i.e. complete, non-compact and without boundary) Alexandrov $n$-space of nonnegative curvature with a soul $S$. In this paper, we will establish several structural results on $X$ that can be viewed as counterparts of structural results on an open Riemannian manifold with nonnegative sectional curvature.