We show that among all the convex bounded domain in R^2 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.
A sharp isoperimetric inequality in the plane involving Hausdorff distance / Alvino, Angelo; Ferone, Vincenzo; Nitsch, Carlo. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 20:(2009), pp. 397-412.
A sharp isoperimetric inequality in the plane involving Hausdorff distance
ALVINO, ANGELO;FERONE, VINCENZO;NITSCH, CARLO
2009
Abstract
We show that among all the convex bounded domain in R^2 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.File | Dimensione | Formato | |
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