, Volume 144, Issue 1, pp 101-114
Date: 13 Jun 2009

A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications

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Abstract

We prove a splitting theorem for Alexandrov space of nonnegative curvature without properness assumption. As a corollary, we obtain a maximal radius theorem for Alexandrov spaces of curvature bounded from below by 1 without properness assumption. Also, we provide new examples of infinite dimensional Alexandrov spaces of nonnegative curvature.