Simple closed geodesics on most Alexandrov surfaces

2013/11/19 by Joël Rouyer, Rouyer, Joël, Costin Vîlcu +1
Mathematics · #53C22 #53C45 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:53C22 #msc:53C45

paper · pdf · doi:10.48550/arxiv.1311.4873

22 pages, 4 figures

arxiv created 2013/11/19 · arxiv updated 2013/11/20

Abstract

We study the existence of simple closed geodesics on most (in the sense of Baire category) Alexandrov surfaces with curvature bounded below, compact and without boundary. We show that it depends on both the curvature bound and the topology of the surfaces.

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