Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order

TL;DR

This paper derives universal eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order on smooth metric measure spaces, extending understanding of spectral properties under curvature constraints.

Contribution

It introduces a general eigenvalue inequality for the buckling problem of the drifting Laplacian of any order on SMMSs, incorporating curvature conditions.

Findings

Established a general eigenvalue inequality for the buckling problem.

Derived universal inequalities under curvature constraints.

Extended spectral analysis to arbitrary order drifting Laplacian.

Abstract

In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully get a general inequality for its eigenvalues. By applying this general inequality, if the complete SMMSs considered satisfy some curvature constraints, we can obtain a universal inequalities for eigenvalues of this buckling problem.