Complex geodesics and iterates of holomorphic maps on convex domains in $\textbf {C}^ n$
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- by Peter R. Mercer PDF
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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 ${{\mathbf {C}}^n}$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 338 (1993), 201-211
- MSC: Primary 32H50; Secondary 32H15, 32H40
- DOI: https://doi.org/10.1090/S0002-9947-1993-1123457-0
- MathSciNet review: 1123457