Closed geodesics in Alexandrov spaces of curvature bounded from above

Details Closed geodesics in Alexandrov spaces of curvature bounded from above Closed geodesics in Alexandrov spaces of curvature bounded from above

2009-09-28

arxiv.org/abs/0909.4981v3

Mathematics

Differential Geometry

Final version, 22 pages, 2 figures, to appear in the Journal of Geometric Analysis

Scientific paper

In this paper, we show a local energy convexity of $W^{1,2}$ 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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