The Schwarz-Pick lemma of high order in several variables
Shaoyu Dai, Huaihui Chen, Yifei Pan
TL;DR
This paper establishes a high order Schwarz-Pick lemma for complex mappings between unit balls, providing new estimates for derivatives based on the Bergman metric, advancing the understanding of geometric function theory in several complex variables.
Contribution
It introduces a high order Schwarz-Pick lemma in multiple complex variables using the Bergman metric, extending classical results to higher derivatives.
Findings
Derived Schwarz-Pick estimates for derivatives of arbitrary order
Extended classical Schwarz-Pick lemma to high order in several variables
Utilized Bergman metric to formulate the lemma
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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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Analytic and geometric function theory