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Parametric representation of univalent mappings in several complex variables
by
Gabriela Kohr
Babes-Bolyai University, Faculty of Mathematics and Computer Sciences, 1 M. Kogalniceanu
Coauthors: Mirela Kohr (Babes-Bolyai University, Faculty of Mathematics and Computer Sciences, 1 M. Kogalniceanu Str., 3400 Cluj-Napoca, Romania.)
Let B be the unit ball of Cn with respect to the Euclidean norm. We investigate a subset of normalized biholomorphic mappings of B which arises in the study of the Loewner differential equation, namely the set S0(B) of mappings which have parametric representation. A key role in our discussion is played by the analog of the Caratheodory set, i.e., the set of holomorphic mappings from B into Cn of ``positive real part''. We consider subsets of S0(B) obtained by placing restrictions on the mapping from the Caratheodory set which occurs in the generalized Loewner differential equation. Also we obtain growth and distortion results as well as coefficient estimates for these subsets of S0(B).
Date received: July 26, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahv-92.