On complex convexity
2008 (English)Doctoral thesis, monograph (Other academic)
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.
ℂ-convex, Linearly convex, Charathéodory metric, Kobayshi metric
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-7449ISBN: 978-91-7155-617-2OAI: oai:DiVA.org:su-7449DiVA: diva2:198302
2008-04-14, sal 14, hus 5, Kräftriket, Stockholm, 10:00
Pflug, Peter, Professor
Passare, Mikael, Professor