DOMAINS WITH Ck CR CONTRACTIONS

Abstract

Let Ω be a domain with smooth boundary in Cn+1 and let p ∈ ∂Ω. Suppose that Ω is Kobayashi hyperbolic and p is of Catlin multi-type τ = (τ0, . . . , τn). In this paper, we show that Ω admits a C k contraction at p with k ≥ |τ | + 1 if and only if Ω is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial.

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