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

Chiara Bianchini; Gisella Croce; Antoine Henrot

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

Optimization and Control 2021-07-23 v2

Authors: Chiara Bianchini , Gisella Croce , Antoine Henrot

Abstract

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.

Keywords

quantitative isoperimetric inequality barycentric asymmetry isoperimetric deficit shape optimization convex sets

Cite

@article{arxiv.1904.02759,
  title  = {On the quantitative isoperimetric inequality in the plane with the barycentric distance},
  author = {Chiara Bianchini and Gisella Croce and Antoine Henrot},
  journal= {arXiv preprint arXiv:1904.02759},
  year   = {2021}
}

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

Abstract

Keywords

Cite

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