Vol. 87, No. 2, 1980

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ISSN: 0030-8730
Holomorphic mapping of products of annuli in Cn

Eric Bedford

Vol. 87 (1980), No. 2, 271–281
Abstract

Let Ω1,Ω2 Cn be bounded pseudoconvex Reinhardt domains with the property that z1zn0 for all (z1,,zn) Ωj. A holomorphic mapping f : Ω1 Ω2 is discussed in terms of the induced mapping on homology f : H11,R) H12,R). Specifically, there is a norm on H1j,R) which must decrease under f. As a consequence we prove that a domain Ω as above is rigid in the sense of H. Cartan: if f : Ω Ω is holomorphic and f : H1,R) H1,R) is nonsingular, then f is an automorphism.

Mathematical Subject Classification 2000
Primary: 32A07
Secondary: 32H99
Milestones
Received: 24 April 1978
Published: 1 April 1980
Authors
Eric Bedford
Department of Mathematics
Indiana University
Rawles Hall 115
Bloomington IN 47405-5701
United States