Moderate smoothness of most Alexandrov surfaces

2013/08/18 by Jin-ichi Itoh, Itoh, Jin-ichi, Joel Rouyer +3
Mathematics · #53C45 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:53C45

paper · pdf · doi:10.48550/arxiv.1308.3862

12 pages, 1 figure. Minor changes for the second version, mainly of linguistic nature

arxiv created 2014/05/17 · arxiv updated 2014/05/20

Abstract

We show that, in the sense of Baire category, most Alexandrov surfaces with curvature bounded below by κ have no conical points. We use this result to prove that at most points of such surfaces, the lower and the upper Gaussian curvatures are equal to κ and ∞ respectively.

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