The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B _p ⁿ of ℂⁿ

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 ℂⁿ. 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 = ∞, respectively.