Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, June 13, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Imre Bárány (Alfréd Rényi Mathematical Institute)

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

What is the minimal perimeter L_n that a convex lattice polygon with n vertices can have? Jarnik proved in 1926 that L_n= (sqrt(6π)/9)n^3/2+O(n^3/4). Here we extend this result to all, not necessarily symmetric, norms in the plane. We also determine the limiting shape of the convex lattice n-gon minimizing the perimeter.

This is joint work with N. Enriquez.

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