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hal-00692991, version 1

On the volume product of polygons

Mathieu Meyer 1, Shlomo Reisner

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG 81, 1 (2011) 93--100

Abstract: 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.

  • 1:  Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
  • Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout
  • Domain : Mathematics/Mathematical Physics
 
  • hal-00692991, version 1
  • http://hal-upec-upem.archives-ouvertes.fr/hal-00692991
  • oai:hal-upec-upem.archives-ouvertes.fr:hal-00692991
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  • Submitted on: Tuesday, 1 May 2012 19:17:29
  • Updated on: Tuesday, 1 May 2012 19:17:30