A Sharp Lower Bound for the Spectrum of the Hodge Laplacian on K\"ahler Hyperbolic Manifolds and its Applications

Abstract

In this paper, we establish a sharp lower bound for the spectrum of the Hodge Laplacian on K\"ahler hyperbolic manifolds. This bound is expressed explicitly in terms of the supremum norm of the 1-form associated with the K\"ahler hyperbolic structure. As an application, we obtain explicit spectral lower bounds for bounded symmetric domains.