dc.contributor.advisor | Gavosto, Estela | |
dc.contributor.author | Console, Alexander | |
dc.date.accessioned | 2014-06-18T03:38:58Z | |
dc.date.available | 2014-06-18T03:38:58Z | |
dc.date.issued | 2013-12-31 | |
dc.date.submitted | 2013 | |
dc.identifier.other | http://dissertations.umi.com/ku:13167 | |
dc.identifier.uri | http://hdl.handle.net/1808/14201 | |
dc.description.abstract | In 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.extent | 85 pages | |
dc.language.iso | en | |
dc.publisher | University of Kansas | |
dc.rights | This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author. | |
dc.subject | Mathematics | |
dc.subject | Complex | |
dc.subject | Variables | |
dc.title | Limit Domains in Several Complex Variables | |
dc.type | Dissertation | |
dc.contributor.cmtemember | Orr, James | |
dc.contributor.cmtemember | Porter, Jack | |
dc.contributor.cmtemember | Sheu, Albert | |
dc.contributor.cmtemember | Torres, Rodolfo | |
dc.thesis.degreeDiscipline | Mathematics | |
dc.thesis.degreeLevel | Ph.D. | |
dc.rights.accessrights | openAccess | |