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arXiv · 2207.06370

A note on existence of an optimal set for a bonnesen type quantitative isoperimetric ratio in the plane

Silvio Bove·Gisella Croce·Giovanni Pisante
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Abstract

In this note we prove the existence of a set $E_0\subset\mathbb{R}^2$, different from a ball, which minimizes, among the convex sets that satisfy a suitable interior cone condition, the ratio \begin{equation} \label{eq:0} \frac{D(E)}{\lambda_\mathcal{H}^2(E)}, \end{equation} where $D$ is the isoperimetric deficit and $\lambda_\mathcal{H}$ the deviation from the spherical shape of a set $E\subset \mathbb{R}^2$.

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Silvio Bove, Gisella Croce, Giovanni Pisante. 2022-07-13. A note on existence of an optimal set for a bonnesen type quantitative isoperimetric ratio in the plane. https://arxiv.org/abs/2207.06370

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