On the volume product of polygons

Mathieu Meyer (1) , Shlomo Reisner

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We present a method that allows us to prove that the volume product of polygons in a"e(2) 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.

Domaines: Physique mathématique [math-ph]

Mathieu Meyer, Shlomo Reisner. On the volume product of polygons. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2011, 81 (1), pp.93--100. ⟨10.1007/s12188-011-0054-3⟩. ⟨hal-00692991⟩