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arXiv · 1507.08189

On The Quantitative Isoperimetric Inequality In The Plane

Chiara Bianchini·Gisella Croce·Antoine Henrot
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Abstract

In this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set $Ω$, different from a ball, which minimizes the ratio $δ(Ω)/λ^2(Ω)$, where $δ$ is the isoperimetric deficit and $λ$ 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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Chiara Bianchini, Gisella Croce, Antoine Henrot. 2015-07-29. On The Quantitative Isoperimetric Inequality In The Plane. https://arxiv.org/abs/1507.08189

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