The most inaccessible point of a convex domain

2010/09/15 by Calvo, Maria, Munoz, Vicente
#52A99 #97G40 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1009.2948

Abstract

The inaccessibility of a point p in a bounded domain D ⊂ Rⁿ is the minimum of the lengths of segments through p with boundary at \bd D. The points of maximum inaccessibility I_D are those where the inaccessibility achieves its maximum. We prove that for strictly convex domains, I_D is either a point or a segment, and that for a planar polygon I_D is in general a point. We study the case of a triangle, showing that this point is not any of the classical notable points.

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