The isodiametric problem for lattice-point-free convex sets

Authors: Hernández Cifre, M.¹; Vassallo, S.²

Source: Acta Mathematica Hungarica, Volume 114, Number 4, March 2007 , pp. 337-355(19)

Publisher: Springer

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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.

Keywords: convex sets; lattice points; isodiametric inequality; 52C05; 52A40

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10474-007-5184-9

Affiliations: 1: Email: mhcifre@um.es 2: Email: salvatore.vassallo@unicatt.it

Publication date: 2007-03-01