Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width

Details Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width

2011-02-06

arxiv.org/abs/1102.1194v1

Discrete and Computational Geometry 47/2 (2012), 275-287

Mathematics

Metric Geometry

17 pages

Scientific paper

10.1007/s00454-011-9369-1

A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a "fat" one, if it contains the centers of its generating balls. The core part of this paper is an extension of Schramm's theorem and its proof on illuminating convex bodies of constant width to the family of "fat" spindle convex bodies.

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