The most inaccessible point of a convex domain

Details The most inaccessible point of a convex domain The most inaccessible point of a convex domain

2010-09-15

arxiv.org/abs/1009.2948v1

Mathematics

Metric Geometry

14 pages, 8 figures

Scientific paper

The inaccessibility of a point p in a bounded domain D \subset R^n 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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