Abstract
The symmetrized bidisc G2 is defined byG2:={(z1+z2,z1z2)âC2:|z1|<1,|z2|<1,z1,z2âC}. It is a bounded inhomogeneous pseudoconvex domain without C1 boundary, and especially the symmetrized bidisc hasn't any strongly pseudoconvex boundary point and the boundary behavior of both CarathĂ©odory and Kobayashi metrics over the symmetrized bidisc is hard to describe precisely. In this paper, we study the boundary Schwarz lemma for holomorphic self-mappings of the symmetrized bidisc G2, and our boundary Schwarz lemma in the paper differs greatly from the earlier related results.
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