11 research outputs found
Closed geodesics in Alexandrov spaces of curvature bounded from above
In this paper, we show a local energy convexity of maps into
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.Comment: Final version, 22 pages, 2 figures, to appear in the Journal of
Geometric Analysi