NDLI: Complex geodesics in convex tube domains II

Content Provider	Springer Nature Link
Author	Zając, Sylwester
Copyright Year	2015
Abstract	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.
Ending Page	1887
Page Count	23
Starting Page	1865
File Format	PDF
ISSN	03733114
e-ISSN	16181891
Journal	Annali di Matematica Pura ed Applicata
Issue Number	6
Volume Number	195
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-10-27
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Invariant metrics and pseudodistances Convex domain Reinhardt domain Complex geodesic Special domains (Reinhardt, Hartogs, circular, tube) Mathematics Tube domain Extremal mapping
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Complex geodesics in convex tube domains II