The Schwarz-Pick lemma of high order in several variables

2011/09/13 by Shaoyu Dai, Dai, Shaoyu, Huaihui Chen +3
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1109.2791

openalex publication_date 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a high order Schwarz-Pick lemma for mappings between unit balls in complex spaces in terms of the Bergman metric. From this lemma, Schwarz-Pick estimates for partial derivatives of arbitrary order of mappings are deduced.

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