Talk:Pseudoconvexity
Add topicLatest comment: 8 months ago by Vaughan Pratt in topic Redirection of Hartogs' domain
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Are all convex sets in C^n pseudoconvex?
[edit]A discussion would be useful.Rich 20:12, 26 November 2006 (UTC)
- Yes, they are. At least if you by convex mean ordinary linear convexity. This is a elementary result which can be found in, Holomorphic functions and integral representations in several complex variables, ISBN 0-387-96259-x, by R. Michael Range Vigfus (talk) 11:02, 29 December 2009 (UTC)
Redirection of Hartogs' domain
[edit]The redirection here of the link Hartogs' domain is somewhat misleading, since those domains are extremely particular pseudoconvex domains, having properties not shared by other kind of set belonging to such class. It is necessary to create separated entry: anyone interested? :D Daniele.tampieri (talk) 14:42, 28 November 2011 (UTC)
- At the very least, there should be a reference somewhere in Wikipedia to Hartogs' involvement, such as a citation to relevant work of Hartogs, or to a book or paper treating Hartogs' domain. As it is, I have no idea where to research this. Vaughan Pratt (talk) 04:11, 23 November 2025 (UTC)
defining functions
[edit]Is it true that the defining function of a Levy pseudoconvex domain can be extended to all of C^n? Shouldn't it rather be a neighborhood of the closure of the Levy pseudoconvex domain? — Preceding unsigned comment added by 129.49.88.228 (talk) 21:07, 15 October 2013 (UTC)