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

被引：8
|
作者：
Mitsuishi, Ayato [1 ]
机构：
[1] Univ Tsukuba, Grad Sch Pure & Appl Sci, Tsukuba, Ibaraki 3058571, Japan
来源：
GEOMETRIAE DEDICATA | 2010年 / 144卷 / 01期
基金：
日本学术振兴会;
关键词：
Alexandrov space; Lower curvature bound; Splitting theorem; Maximal radius sphere theorem; Infinite dimension;
D O I：
10.1007/s10711-009-9390-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：101 / 114
页数：14
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