# Lipschitz continuity of holomorphic mappings with respect to Bergman metric

## TL;DR

This paper establishes sharp Lipschitz continuity estimates for holomorphic mappings concerning the Bergman metric, improving and generalizing previous results in the field.

## Contribution

It provides the most precise Lipschitz estimates with respect to the Bergman metric for holomorphic mappings, extending earlier work.

## Key findings

- Sharp Lipschitz continuity estimates derived
- Results improve previous bounds by Ghatage, Yan, and Zheng
- Generalization to broader classes of holomorphic mappings

## Abstract

n this paper, we establish the sharp estimate of the Lipschitz continuity with respect to the Bergman metric. The obtained results are the improvement and generalization of the corresponding results of Ghatage, Yan and Zheng (Proc. Amer. Math. Soc., 129: 2039-2044, 2000).