Silvio Bove | Searcharxiv

arXiv2026

An existence result for a quantitative isoperimetric inequality in $\mathbb{R}^3$ involving the Hausdorff asymmetry

We study the existence of an optimizer for a quantitative isoperimetric ratio $\mathcal{Q}_*$ in $\mathbb{R}^3$ involving the Hausdorff asymmetry. We prove that $\mathcal{Q}_*$ attains its minimum over the class $\mathcal{A}$ of convex bodies of fixed volume.

math.OC↗

arXiv2022

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

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)}{λ_\mathcal{H}^2(E)}, \end{equation} where $D$ is the isoperimetric deficit and $λ_\mathcal{H}$ the deviation from the spherical shape of a set $E\subset \mathbb{R}^2$.

math.OC↗