Some isoperimetric inequalities with application to the Stekloff problem

TL;DR

This paper establishes isoperimetric inequalities related to moments of inertia and applies them to derive bounds for the eigenvalues of the Stekloff problem in Euclidean space.

Contribution

It introduces new isoperimetric inequalities for moments of inertia and applies these results to eigenvalue problems, specifically the Stekloff problem.

Findings

Isoperimetric inequalities for moments of inertia established.

Derived an inequality for the product of Stekloff eigenvalues.

Provides bounds for eigenvalues based on geometric properties.

Abstract

In this paper we establish isoperimetric inequalities for the product of some moments of inertia. As an application, we obtain an isoperimetric inequality for the product of the $N$ first nonzero eigenvalues of the Stekloff problem in $\mathbb{R}^N$.