<p>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 <i>C</i><sup>1</sup>. The study of Hartogs domains also leads to characterization theorem of bounded ℂ-convex domains with <i>C</i><sup>1</sup> 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 <i>C</i><sup>2</sup> boundary. We also show an exhaustion theorem for bounded ℂ-convex domains with <i>C</i><sup>2</sup> boundary. This theorem is later applied, giving a generalization of a theorem of L. Lempert concerning the relation between the Carathéodory and Kobayashi metrics.</p>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:su-7449 |
| Date | January 2008 |
| Creators | Jacquet, David |
| Publisher | Stockholm University, Department of Mathematics, Stockholm : Matematiska institutionen |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Doctoral thesis, monograph, text |
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