JournalsrlmVol. 20, No. 4pp. 397–412

A sharp isoperimetric inequality in the plane involving Hausdorff distance

  • 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
A sharp isoperimetric inequality in the plane involving Hausdorff distance cover
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Abstract

We show that among all the convex bounded domain in ℝ2 having an assigned asymmetry index related to Hausdorff distance, 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 involving Hausdorff distance. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 4, pp. 397–412

DOI 10.4171/RLM/555