A sharp isoperimetric inequality in the plane
Angelo Alvino
Università degli Studi di Napoli Federico II, ItalyVincenzo Ferone
Università degli Studi di Napoli Federico II, ItalyCarlo Nitsch
Università degli Studi di Napoli Federico II, Italy
Abstract
We show that among all the convex bounded domain in 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
Angelo Alvino, Vincenzo Ferone, Carlo Nitsch, A sharp isoperimetric inequality in the plane. J. Eur. Math. Soc. 13 (2011), no. 1, pp. 185–206
DOI 10.4171/JEMS/248