The isodiametric problem in the Euclidean plane is solved for lattice-point-free convex sets: we characterize the planar convex sets containing no points of the rectangular lattice in their interior, which have maximum area, for each given value of the diameter. Then we use this result for giving also an answer to the isodiametric problem in the case of an arbitrary lattice.
Vassallo, S. F., Hernandez Cifre, M., The isodiametric problem for lattice-point-free convex sets, <<ACTA MATHEMATICA HUNGARICA>>, 2007; (114 (4)): 337-355 [http://hdl.handle.net/10807/29375]
The isodiametric problem for lattice-point-free convex sets
Vassallo;
2007
Abstract
The isodiametric problem in the Euclidean plane is solved for lattice-point-free convex sets: we characterize the planar convex sets containing no points of the rectangular lattice in their interior, which have maximum area, for each given value of the diameter. Then we use this result for giving also an answer to the isodiametric problem in the case of an arbitrary lattice.
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