The magic functions and automorphisms of a domain

Details The magic functions and automorphisms of a domain The magic functions and automorphisms of a domain

2007-09-02

arxiv.org/abs/0709.0096v2

Mathematics

Complex Variables

17 pages. This version contains an additional proposition (2.11) and some minor corrections, notably to Propositions 3.6 and 3

Scientific paper

We introduce the notion of magic functions of a general domain in
d-dimensional complex space and show that the set of magic functions of a given
domain is an intrinsic complex-geometric object. We determine the set of magic
functions of the symmetrised bidisc G, and thereby find all automorphisms of G
and a formula for the Caratheodory distance on G.

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