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arXiv · 0909.4981

Closed geodesics in Alexandrov spaces of curvature bounded from above

Longzhi Lin
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Abstract

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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Longzhi Lin. 2009-09-28. Closed geodesics in Alexandrov spaces of curvature bounded from above. https://doi.org/10.1007/s12220-010-9153-0

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