Complex geodesics in convex tube domains II
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- 作者：Sylwester Zając
- 关键词：Complex geodesic ; Tube domain ; Convex domain ; Reinhardt domain ; Extremal mapping
- 刊名：Annali di Matematica Pura ed Applicata
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：195
- 期：6
- 页码：1865-1887
- 全文大小：614 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1618-1891
- 卷排序：195
文摘
Complex geodesics are fundamental constructs for complex analysis and as such constitute one of the most vital research objects within this discipline. In this paper, we formulate a rigorous description, expressed in terms of geometric properties of a domain, of all complex geodesics in a convex tube domain in \({\mathbb {C}}^n\) containing no complex affine lines. Next, we illustrate the obtained result by establishing a set of formulas stipulating a necessary condition for extremal mappings with respect to the Lempert function and the Kobayashi–Royden metric in a large class of bounded, pseudoconvex, complete Reinhardt domains: for all of them in \({\mathbb {C}}^2\) and for those in \({\mathbb {C}}^n\) whose logarithmic image is strictly convex in the geometric sense.