29 research outputs found
Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width
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.Comment: 17 page