Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain

TL;DR

This paper introduces two new universal inequalities that bound Neumann eigenvalues of the Laplacian for planar convex domains, advancing the understanding of spectral properties in geometric analysis.

Contribution

The paper presents novel universal inequalities for Neumann eigenvalues, providing new bounds applicable to all planar convex domains.

Findings

Established two new universal inequalities for Neumann eigenvalues.

Provided bounds that are independent of specific domain shapes.

Enhanced understanding of spectral geometry for convex domains.

Abstract

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