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Pré-Publication, Document De Travail Année : 2019

On the quantitative isoperimetric inequality in the plane with the barycentric distance

Chiara Bianchini
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Antoine Henrot
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Résumé

In this paper we study the following quantitative isoperimetric inequality in the plane: $\lambda_0^2(\Omega) \leq C \delta(\Omega)$ where $\delta$ is the isoperimetric deficit and $\lambda_0$ is the barycentric asymmetry. Our aim is to generalize some results obtained by B. Fuglede in \cite{Fu93Geometriae}. For that purpose, we consider the shape optimization problem: minimize the ratio $\delta(\Omega)/\lambda_0^2(\Omega)$ in the class of compact connected sets and in the class of convex sets.
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Dates et versions

hal-02090603 , version 1 (04-04-2019)
hal-02090603 , version 2 (26-07-2021)

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  • HAL Id : hal-02090603 , version 1

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Chiara Bianchini, Gisella Croce, Antoine Henrot. On the quantitative isoperimetric inequality in the plane with the barycentric distance. 2019. ⟨hal-02090603v1⟩
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