Closed Geodesics in Alexandrov Spaces of Curvature Bounded from Above

被引：1
|
作者：
Lin, Longzhi [1 ]
机构：
[1] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2011年 / 21卷 / 02期
关键词：
Width; Sweepout; Min-max; Closed geodesic; Alexandrov space of curvature bounded from above; EXTINCTION TIME; WIDTH;
D O I：
10.1007/s12220-010-9153-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show a local energy convexity of W-1,W-2 maps into CAT(K) spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout construction to produce closed geodesics in any closed Alexandrov space of curvature bounded from above, which also provides a generalized version of the Birkhoff-Lyusternik theorem on the existence of non-trivial closed geodesics in the Alexandrov setting.
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页码：429 / 454
页数：26
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