In this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set $Omega$, different from a ball, which minimizes the ratio $delta(Omega)/lambda^2(Omega)$, where $delta$ is the isoperimetric deficit and $lambda$ the Fraenkel asymmetry, giving a new proof ofthe quantitative isoperimetric inequality. Some new properties of the optimal set are also shown.
On The Quantitative Isoperimetric Inequality In The Plane / Chiara Bianchini; Gisella Croce; Antoine Henrot. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 23:(2017), pp. 517-549. [10.1051/cocv/2016002]
On The Quantitative Isoperimetric Inequality In The Plane
BIANCHINI, CHIARA;
2017
Abstract
In this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set $Omega$, different from a ball, which minimizes the ratio $delta(Omega)/lambda^2(Omega)$, where $delta$ is the isoperimetric deficit and $lambda$ the Fraenkel asymmetry, giving a new proof ofthe quantitative isoperimetric inequality. Some new properties of the optimal set are also shown.
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