A quantitative Weinstock inequality

TL;DR

This paper investigates a quantitative version of the Weinstock inequality for the first non-trivial Steklov eigenvalue in higher dimensions, utilizing a new isoperimetric inequality involving boundary momentum, volume, and perimeter of convex sets.

Contribution

It introduces a novel quantitative isoperimetric inequality that relates boundary momentum, volume, and perimeter, advancing the understanding of Steklov eigenvalues in convex geometry.

Findings

Established a quantitative Weinstock inequality in higher dimensions.

Linked Steklov eigenvalues to geometric properties of convex sets.

Provided bounds involving boundary momentum, volume, and perimeter.

Abstract

The paper is devoted to the study of a quantitative Weinstock inequality in higher dimension for the first non trivial Steklov eigenvalue of Laplace operator for convex sets. The key rule is played by a quantitative isoperimetric inequality which involves the boundary momentum, the volume and the perimeter of a convex open set of $\mathbb R^n$, $n \ge 2$.