2014/11/03 by Yang Liu, Zhihua Chen, Liu, Yang +3
Mathematics · #30C80 #32H02 #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.1411.0600
openalex publication_date 2014/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give a general boundary Schwarz lemma for holomorphic mappings between unit balls in any dimensions. It is proved that if the mapping f∈ C1+α at z0∈ ∂ \mathbb Bn with f(z0)=w0∈ ∂ \mathbb BN for any n,N≥ 1, then the Jacobian matrix Jf(z0) maps the tangent space Tz0(∂ \mathbb Bn) to Tw0(∂ \mathbb BN), and the holomorphic tangent space T(1,0)z0(∂ \mathbb Bn) to T(1,0)w0(∂ \mathbb BN) as well.