Jarnik's convex lattice $n$-gon for non-symmetric norms

Imre Barany (1, 2) , Nathanael Enriquez (3, 4)

1 Alfréd Rényi Institute of Mathematics
2 Department of Mathematics UCL
3 MODAL'X - Modélisation aléatoire de Paris X
4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

What is the minimum perimeter of a convex lattice $n$-gon? This question was answered by Jarnik in 1926. We solve the same question in the case when perimeter is measured by a (not necessarily symmetric) norm.

Mots clés: convex lattice polygon; isoperimetric problem; variational problem

Domaines: Géométrie métrique [math.MG]

Imre Barany, Nathanael Enriquez. Jarnik's convex lattice $n$-gon for non-symmetric norms. 2009. ⟨hal-00434287⟩