Infimum of the spectrum of Laplace-Beltrami operator on Cartan classical domains of type Ⅲ and Ⅳ

Abstract

<abstract><p>Let $ R_{{\cal A}} $ be the Cartan classical domains of type Ⅲ and Ⅳ, and $ \Delta_g $ is assumed to be the Laplace-Beltrami operator associated to the Bergman metric $ g $ on $ R_{{\cal A}} $. In this paper, we derive an estimate for $ \lambda_1(\Delta_g) $, which is the bottom of the spectrum of $ \Delta_g $ on $ R_{{\cal A}} $.</p></abstract>