Contraction property on complex hyperbolic ball

TL;DR

This paper establishes an isoperimetric inequality on the complex hyperbolic ball and demonstrates a contraction property for holomorphic functions in Hardy and weighted Bergman spaces, generalizing previous results.

Contribution

It introduces a new isoperimetric inequality on the complex hyperbolic ball and extends contraction properties of holomorphic functions under this setting.

Findings

Proved an isoperimetric inequality on the complex hyperbolic ball.

Established a contraction property for holomorphic functions in Hardy and weighted Bergman spaces.

Generalized Kulikov's results to higher-dimensional complex hyperbolic spaces.

Abstract

We prove an isoperimetric inequalitie on the complex hyperbolic ball with Assumption \ref{assumption}}. As an application, we prove a contraction property for the holomorphic functions in Hardy and weighted Bergman spaces on the complex hyperbolic ball with this assumption. The results can be seen as partial generalization of Kulikov's result on the complex hyperbolic plane.