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
email: brass@inf.fu-berlin.de

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.

Get the report here or by anonymous ftp: 
Server: fubinf.inf.fu-berlin.de
File:   pub/reports/tr-b-97-05.ps.gz