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dc.contributor.advisorGavosto, Estela
dc.contributor.authorConsole, Alexander
dc.date.accessioned2014-06-18T03:38:58Z
dc.date.available2014-06-18T03:38:58Z
dc.date.issued2013-12-31
dc.date.submitted2013
dc.identifier.otherhttp://dissertations.umi.com/ku:13167
dc.identifier.urihttp://hdl.handle.net/1808/14201
dc.description.abstractIn this thesis we demonstrated the existence of domains in C^2 evidencing both intrinsic phenomena of C^n, n 1, and different types of boundary smoothness. We constructed these domains by taking limits of preimages of polydiscs under a sequence of shears selected to control boundary smoothness. Unlike the complex plane, in C^n there are simply connected domains that are biholomorphic to C^n but are proper subsets of C^n. These domains are called FatouBieberbach domains and they arise naturally in the study of complex dynamics. We showed that there exists a Fatou-Bieberbach domain in C^2 with Gevrey smooth boundary. Another interesting occurrence in C^2 is the existence of simply connected proper subsets of C^2 that are not biholomorphic to the unit ball nor biholomorphic to C^2. Onesuch class are Short-C^2 domains. We constructed Short-C^2 domains with C-infinity boundary and Short-C^2 domains with prescribed local C^l boundary smoothness and controlled geometry.
dc.format.extent85 pages
dc.language.isoen
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.subjectComplex
dc.subjectVariables
dc.titleLimit Domains in Several Complex Variables
dc.typeDissertation
dc.contributor.cmtememberOrr, James
dc.contributor.cmtememberPorter, Jack
dc.contributor.cmtememberSheu, Albert
dc.contributor.cmtememberTorres, Rodolfo
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelPh.D.
dc.rights.accessrightsopenAccess


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