By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit $p$-ball $B_{p}^{n}$ of $\mathbb{C}^n$. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on $B_{p}^{n}$ is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for $p=2$, and the unit polydisk for $p=\infty$, respectively.
Jianfei WANG
,
Yanhui ZHANG
. THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS $B_{p}^{n}$ OF $\mathbb{C}^{n}$p OF Cn[J]. Acta mathematica scientia, Series B, 2024
, 44(3)
: 839
-850
.
DOI: 10.1007/s10473-024-0304-y
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