Journal of Geometric Analysis

, Volume 21, Issue 2, pp 429–454 | Cite as

Closed Geodesics in Alexandrov Spaces of Curvature Bounded from Above

Article

Abstract

In this paper, we show a local energy convexity of W1,2 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.

Keywords

Width Sweepout Min-max Closed geodesic Alexandrov space of curvature bounded from above 

Mathematics Subject Classification (2000)

53C23 58E10 53C22 

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Copyright information

© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  1. 1.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA

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