On the maximal mean curvature of a smooth surface

2016/04/20 by Vincenzo Ferone, Carlo Nitsch, Ferone, Vincenzo +3
Mathematics · #35P15 #53A05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC) #math.DG #math.OC #msc:35P15 #msc:53A05 #msc:53A10

paper · pdf · doi:10.48550/arxiv.1604.06042

arxiv created 2016/04/20 · arxiv updated 2016/04/21

Abstract

Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the maximal curvature alone. We show that in higher dimensions this is not true, and for a given maximal mean curvature we provide smooth embeddings of the ball with arbitrary small volume.

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