A Generalization of Zalcman's Lemma on Complex Lie Groups

TL;DR

This paper extends Zalcman's Lemma, a key tool in complex analysis, to complex Lie groups using exponential mappings from holomorphic one-parameter subgroups, broadening its applicability.

Contribution

The paper introduces a generalization of Zalcman's Lemma tailored for complex Lie groups via exponential mappings, expanding its theoretical scope.

Findings

Generalization of Zalcman's Lemma to complex Lie groups

Application of exponential mappings in the generalization

Potential new tools for complex dynamics and normal families

Abstract

Zalcman's Lemma makes significant applications in normal families, complex dynamics and related problems in complex analysis. In the present paper, we are devoted to generalizing the classical Zalcman's lemma to complex Lie groups by means of exponential mappings defined by holomorphic one-parameter subgroups.