A Generalization of Zalcman's Lemma on Complex Lie Groups

2025/11/25 by Dong, Xianjing, Lv, Yanda
#32A19 #32H02 #32H25 #Complex Variables (math.CV) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2511.20536

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.

Citations

• An improvement of Zalcman's lemma in Cⁿ

Related

• The Cartan exponential map in semi-simple compact Lie groups
• Calderón-Zygmund theory on some Lie groups of exponential growth
• Some Normality Criteria for Families of Holomorphic Functions of Several Complex Variables
• Calderon Zygmund decompositions on amenable groups
• An improvement of Zalcman's lemma in Cⁿ