A boundary Schwarz lemma for holomorphic mappings from the polydisc to the unit ball
Yang Liu, Zhihua Chen, Yifei Pan
TL;DR
This paper establishes a boundary Schwarz lemma for holomorphic mappings from polydiscs to unit balls, generalizing the classical boundary Schwarz lemma in one complex variable to higher dimensions.
Contribution
It introduces a general boundary Schwarz lemma applicable to multi-dimensional holomorphic mappings from polydiscs to unit balls, extending classical results.
Findings
Proves a boundary Schwarz lemma in multiple dimensions
Recovers the classical boundary Schwarz lemma in one variable
Provides a unified framework for boundary behavior of holomorphic maps
Abstract
In this paper, we prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary Schwarz lemma.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Meromorphic and Entire Functions