Disk Packings which have Non-Extreme Exponents

Abstract

Let U be an open set in the Euclidean plane which has finite area. A complete (or solid) packing of U is a sequence of pairwise disjoint open disks C={Dn}, each contained in U and whose total area equals that of U. A simple osculatory packing of U is one in which the disk Dn has, for each n, the largest radius of disks contained in (S- denotes the closure of the set U.) If rn is the radius of Dn, then the exponent of the packing, e(C, U) is the infimum of real numbers t for which In the sequel we refer to a complete packing simply as a packing.