Minkowski Circle Packings on the Sphere

We consider n caps on the sphere such that none of them contains in its interior the center of another. We give an upper bound for the total area of the caps, which is sharp for n = 3 , 4, 6, and 12 and is asymptotically sharp for great values of n . Received September 11, 1997, and in revised form March 2, 1998.