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.

引用

页码：101 / 114

页数：14

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