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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Complex geodesics and iterates of holomorphic maps on convex domains in $ {\bf C}\sp n$


Author: Peter R. Mercer
Journal: Trans. Amer. Math. Soc. 338 (1993), 201-211
MSC: Primary 32H50; Secondary 32H15, 32H40
MathSciNet review: 1123457
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Abstract: We study complex geodesics $ f:\Delta \to \Omega $, where $ \Delta $ is the unit disk in $ {\mathbf{C}}$ and $ \Omega $ belongs to a class of bounded convex domains in $ {{\mathbf{C}}^n}$ with no boundary regularity assumption. Along with continuity up to the boundary, existence of such complex geodesics with two prescribed values $ z$, $ w \in \bar \Omega $ is established. As a consequence we obtain some new results from iteration theory of holomorphic self maps of bounded convex domains in $ {{\mathbf{C}}^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1123457-0
PII: S 0002-9947(1993)1123457-0
Article copyright: © Copyright 1993 American Mathematical Society