On the paper "The Payne conjecture for Dirichlet and buckling eigenvalues", by Genquian Liu

TL;DR

This note reviews the problem related to the Payne conjecture for Dirichlet and buckling eigenvalues and identifies an error in the previous work by G. Liu.

Contribution

The paper clarifies the issue in Liu's work by pinpointing the specific error in his analysis of the Payne conjecture.

Findings

Identification of an error in Liu's proof

Clarification of the problem's current status

Guidance for future research directions

Abstract

The paper by G. Liu [arxiv:2109.02561] contains an error. In this note, I give a brief review of the problem and indicate what the error is.