Blaschke's rolling ball theorem and the Trudinger-Wang monotone bending

2015/12/27 by Aram L. Karakhanyan, Karakhanyan, Aram L.
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1512.08161

arxiv created 2015/12/27 · arxiv updated 2015/12/29

Abstract

We revisit the classical rolling ball theorem of Blaschke for convex surfaces with positive curvature and show that it is linked to another inclusion principle in the optimal mass transportation theory due to Trudinger and Wang. We also discuss an application to reflector antennae design problem.

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