A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications
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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.
KeywordsAlexandrov space Lower curvature bound Splitting theorem Maximal radius sphere theorem Infinite dimension
Mathematics Subject Classification (2000)53C20 53C21
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