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We prove that the highest density of non-overlapping translates of a givencentrally symmetric convex domain relative to its outer parallel domain ofgiven outer radius is attained by a lattice packing in the Euclidean plane.This generalizes some earlier (classical) results. Sharp upper bounds areproved for the analogue problem on congruent circular disks in the spherical(resp., hyperbolic) plane and on congruent balls in Euclidean $3$-space.

Density bounds for unit ball packings relative to their outer parallel domains