Densest packing of translates of the union of two circles (Q1084676)

Let \(d(u)\) (resp. \(\bar d(u))\) denote the density of the densest packing (resp. lattice packing) of translates of the domain u. An open conjecture is that if u is the union of two convex domains having a point in common, then \(d(u)=\bar d(u)\). The author proves this in the case where u is the union of two unit-radius circular discs whose centers have distance at most 2. The paper closes with two conjectures --- one for lattice packings of translates of unions of unit discs, the other for packings of congruent copies of a domain.