Abstract
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. A spindle convex body is called a “fat” one if it contains the centers of its generating balls. The main result of this paper is a proof of the illumination conjecture for “fat” spindle convex bodies in dimensions greater than or equal to 15.
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