The first Neumann eigenvalue and the width

TL;DR

This paper establishes a precise lower bound for the first Neumann eigenvalue of convex planar domains based on their diameter and width, providing a key geometric spectral inequality.

Contribution

It introduces a sharp lower bound for the first Neumann eigenvalue in terms of geometric parameters of convex domains, advancing spectral geometry understanding.

Findings

Derived a sharp lower bound for the first Neumann eigenvalue

Connected spectral properties to geometric measures like diameter and width

Enhanced the understanding of eigenvalue estimates for convex domains

Abstract

We prove the sharp lower bound of the first Neumann eigenvalue for bounded convex planar domain in term of its diameter and width.