Weighted Perimeters and pth Moments of Inertia of Convex Curves and Surfaces

Gyula Csató, Davide Giovagnoli, Prosenjit Roy

We study a shape optimization problem among convex bodies in ${\mathbb{R}}^n$ that minimize or maximize weighted perimeters of the form $\int_{\partialΩ} ϕ(|x|) \, \mathrm{d} H^{n-1}…