Isoperimetric Inequalities for Densities of Lattice-Periodic Sets

 The minimum boundary length density of a lattice-periodic set with given period lattice and area density is determined, together with the extremal sets, and a conjecture on the higher-dimensional analogue is made. This improves previous results of Hadwiger for -periodic d-dimensional sets and of Schnell and Wills on two-dimensional sets with arbitrary period-lattice.