Choi-Wang inequality for affine connections

TL;DR

This paper extends the Choi-Wang inequality, originally for Laplacian eigenvalues on minimal hypersurfaces, to the setting of affine connections with positive Ricci curvature, broadening its applicability.

Contribution

It generalizes the Choi-Wang inequality to affine connections with positive Ricci curvature, a novel extension beyond the classical Riemannian case.

Findings

Established a lower bound for eigenvalues in the affine connection setting

Extended classical inequalities to new geometric contexts

Provided theoretical framework for affine Ricci curvature analysis

Abstract

Choi-Wang established a lower bound for the first non-zero eigenvalue of the Laplacian on minimal hypersurfaces in manifolds with positive Ricci curvature. We extend this Choi-Wang type inequality to the setting of positive Ricci curvature with respect to the Li-Xia type affine connection.