Bounds for Laplace eigenvalues of Kaehler metrics

TL;DR

This paper establishes new inequalities for Laplace eigenvalues on Kähler manifolds, extending classical results to higher eigenvalues and analytic varieties, providing broader bounds in geometric analysis.

Contribution

It generalizes the classical first eigenvalue inequality to higher eigenvalues and applies similar bounds to analytic varieties within Kähler manifolds.

Findings

Derived inequalities for higher Laplace eigenvalues on Kähler manifolds

Extended eigenvalue bounds to analytic varieties in Kähler settings

Generalized classical eigenvalue inequalities to broader geometric contexts

Abstract

We prove inequalities for Laplace eigenvalues of Kaehler manifolds generalising to higher eigenvalues the classical inequality for the first Laplace eigenvalue due to Bourguignon, Li, and Yau in 1994. We also obtain similar inequalities for analytic varieties in Kaehler manifolds.