Vol. 44, No. 2, 1973

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Starlike and convex mappings in several complex variables

Keizō Kikuchi

Vol. 44 (1973), No. 2, 569–580

In this paper, using the Bergman kernel function KD(z,z), we give necessary and sufficient conditions that a pseudoconformal mapping f(z) be starlike or convex in some bounded schlicht domain D for which the kernel function KD(z,z) becomes infinitely large when the point z D approaches the boundary of D in any way. We also consider starlike and convex mappings from the polydisk or unit hypersphere into Cn.

Mathematical Subject Classification 2000
Primary: 32H10
Secondary: 32A30, 30A32
Received: 21 October 1972
Published: 1 February 1973
Keizō Kikuchi