The most inaccessible point of a convex domain

Maria Calvo; Vicente Munoz

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arXiv · 1009.2948

The most inaccessible point of a convex domain

Maria Calvo·Vicente Munoz

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Abstract

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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BibTeX RIS

Maria Calvo, Vicente Munoz. 2010-09-15. The most inaccessible point of a convex domain. https://arxiv.org/abs/1009.2948

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