Covering Large Balls with Convex Sets in Spherical Space

Abstract

If the n-dimensional unit sphere is covered by finitely many spherically convex bodies, then the sum of the inradii of these bodies is at least π. This bound is sharp, and the equality case is characterized.

7 pages

References in corpus (1)

• The plank problem for symmetric bodies

Cited by in corpus (2)

• A cap covering theorem
• Volumetric bounds for intersections of congruent balls