A sharp isoperimetric inequality in the plane

  • Carlo Nitsch

    Università degli Studi di Napoli Federico II, Italy
  • Angelo Alvino

    Università degli Studi di Napoli Federico II, Italy
  • Vincenzo Ferone

    Università degli Studi di Napoli Federico II, Italy

Abstract

We show that among all the convex bounded domain in ℝ2 having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domain.

Cite this article

Carlo Nitsch, Angelo Alvino, Vincenzo Ferone, A sharp isoperimetric inequality in the plane. J. Eur. Math. Soc. 13 (2011), no. 1, pp. 185–206

DOI 10.4171/JEMS/248