A sharp isoperimetric inequality in the plane involving Hausdorff distance
Carlo Nitsch
Università degli Studi di Napoli Federico II, ItalyAngelo Alvino
Università degli Studi di Napoli Federico II, ItalyVincenzo Ferone
Università degli Studi di Napoli Federico II, Italy

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