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arXiv · 1904.02759

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

Chiara Bianchini·Gisella Croce·Antoine Henrot
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Abstract

In this paper we study the following quantitative isoperimetric inequality in the plane: $λ_0^2(Ω) \leq C δ(Ω)$ where $δ$ is the isoperimetric deficit and $λ_0$ 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 $δ(Ω)/λ_0^2(Ω)$ in the class of compact connected sets and in the class of convex sets.

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Chiara Bianchini, Gisella Croce, Antoine Henrot. 2021-07-22. On the quantitative isoperimetric inequality in the plane with the barycentric distance. https://arxiv.org/abs/1904.02759

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