Date: 05 Apr 2011

On the volume product of polygons

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Abstract

We present a method that allows us to prove that the volume product of polygons in ℝ2 with at most n vertices is bounded from above by the volume product of regular polygons with n vertices. The same method shows that the volume product of polygons is bounded from below by the volume product of triangles (or parallelograms in the centrally symmetric case). These last results give a new proof of theorems of K. Mahler. The cases of equality are completely described.

Communicated by V. Cortés.
Both authors were supported in part by the France-Israel Research Network Program in Mathematics.