A note on the distribution of Neumann eigenvalues of the Laplacian on a Euclidean convex domain

TL;DR

This paper presents universal inequalities for Neumann eigenvalues of the Laplacian on convex domains in Euclidean space, providing new bounds that apply broadly across such geometries.

Contribution

It introduces two universal inequalities for Neumann eigenvalues, advancing understanding of spectral properties of the Laplacian on convex domains.

Findings

Established two universal inequalities for Neumann eigenvalues.

Provided bounds that are applicable to all Euclidean convex domains.

Abstract

We establish two universal inequalities for Neumann eigenvalues of the Laplacian on a Euclidean convex domain.