On the volume product of polygons

  • Mathieu Meyer
  • Shlomo ReisnerEmail author


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.


Convex bodies Volume-product Polygons Affinely-regular 

Mathematics Subject Classification (2010)



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© Mathematisches Seminar der Universität Hamburg and Springer 2011

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050)Université Paris-Est Marne-la-ValléeMarne-la-Vallée cedex 2France
  2. 2.Department of MathematicsUniversity of HaifaHaifaIsrael

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