On the volume product of polygons

Mathieu Meyer, Shlomo Reisner

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)93-100
Number of pages8
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Issue number1
StatePublished - Apr 2011


  • Affinely-regular
  • Convex bodies
  • Polygons
  • Volume-product

ASJC Scopus subject areas

  • General Mathematics


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