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Let Ω be a smoothly bounded domain in Cn such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω at 0 in terms of the Hölder exponent of its Perron-Bremermann function with simple boundary data. We then use this to show that a smoothly bounded domain in C2 is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Hölder continuous boundary data is Hölder continuous.

Domains of finite type and Hölder continuity of the Perron-Bremermann function