Logarithmically convex domain: Difference between revisions
(New page: ==Definition== A domain (connected open subset) in <math>\mathbb{C}</math> is termed '''logarithmically convex''' or '''log-convex''' if we can choose a branch of the logarithm th...) |
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Latest revision as of 19:16, 18 May 2008
Definition
A domain (connected open subset) in is termed logarithmically convex or log-convex if we can choose a branch of the logarithm that is well-defined on this domain, and under which the image of this domain is a convex subset of .
Facts
- Disc away from origin is logarithmically convex: Any disc away from the origin (i.e. not containing the origin in either the boundary or the interior) is logarithmically convex.