Explicit lower bound of the first eigenvalue of the Laplacian on K\"ahler manifolds

TL;DR

This paper derives an explicit lower bound for the first eigenvalue of the Laplacian on K"ahler manifolds, depending on geometric properties like diameter, curvature, and dimension, extending comparison results.

Contribution

It provides a new explicit lower bound for the first Laplacian eigenvalue on K"ahler manifolds based on geometric comparison techniques.

Findings

Explicit lower bound depending on diameter, curvature, and dimension

Extension of Li and Wang's comparison results to eigenvalue estimates

Applicable to a broad class of K"ahler manifolds

Abstract

We establish an explicit lower bound of the first eigenvalue of the Laplacian on K\"ahler manifolds based off the comparison results of Li and Wang. The lower bound will depend on the diameter, dimension, holomorphic sectional curvature and orthogonal Ricci curvature.