On the Holomorphicity of Isometries of Intrinsic Metrics in Complex Analysis
نویسندگان
چکیده
Let Ω1 and Ω2 be strongly pseudoconvex domains in C and f : Ω1 → Ω2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C map to Ω̄1. We then prove that f |∂Ω1 : ∂Ω1 → ∂Ω2 is a CR or anti-CR diffeomorphism. It follows that Ω1 and Ω2 must be biholomorphic or anti-biholomorphic. The main tool is a metric version of the Pinchuk rescaling technique.
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