Vol. 41, No. 3, 1972

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On pseudo-conformal mappings of circular domains

Stefan Bergman

Vol. 41 (1972), No. 3, 579–585

In the present paper we investigate the condition whether the bounded domain B of C2 is a pseudo-conformal image of a circular domain, say C. Under the assumption that this is the case and that the invariant JB(z1,z2;z1,z2) is not a constant, we characterize the center of a circular domain. This characterization is invariant with respect to pseudoconformal transformations. Assuming that B is a pseudoconformal image of a circular domain C and that there is in B one and only one point, say (t1,t2) which satisfies the conditions mentioned above, we determine the representative R(B;t1,t2) of B. If B is a pseudo-conformal image of a circular domain C and (t1,t2) is the image in B of the center of C, then the representive R(B;t1,t2) is a circular domain. The pair of functions v10,v01 mapping B onto R(B;t1,t2) can be written explicitly in terms of the kernel function of B.

Mathematical Subject Classification
Primary: 32H05
Received: 8 July 1971
Published: 1 June 1972
Stefan Bergman