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On complex convexity
Stockholm University, Faculty of Science, Department of Mathematics.
2008 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

This thesis is about complex convexity. We compare it with other notions of convexity such as ordinary convexity, linear convexity, hyperconvexity and pseudoconvexity. We also do detailed study about ℂ-convex Hartogs domains, which leads to a definition of ℂ-convex functions of class C1. The study of Hartogs domains also leads to characterization theorem of bounded ℂ-convex domains with C1 boundary that satisfies the interior ball condition. Both the method and the theorem is quite analogous with the known characterization of bounded ℂ-convex domains with C2 boundary. We also show an exhaustion theorem for bounded ℂ-convex domains with C2 boundary. This theorem is later applied, giving a generalization of a theorem of L. Lempert concerning the relation between the Carathéodory and Kobayashi metrics.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen , 2008. , 76 p.
Keyword [en]
ℂ-convex, Linearly convex, Charathéodory metric, Kobayshi metric
National Category
Research subject
URN: urn:nbn:se:su:diva-7449ISBN: 978-91-7155-617-2OAI: diva2:198302
Public defence
2008-04-14, sal 14, hus 5, Kräftriket, Stockholm, 10:00
Available from: 2008-03-19 Created: 2008-03-19Bibliographically approved

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