Isoperimetric Inequalities for densities of lattice-periodic sets

Peter Braß
Graduiertenkolleg Algorithmische Diskrete Mathematik
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin, Germany

Report B 97-05
June 1997

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 d-dimensional sets with integer period lattice and of Schnell and Wills on twodimensional sets with arbitrary period-lattice.

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