Limit Domains in Several Complex Variables
Issue Date
2013-12-31Author
Console, Alexander
Publisher
University of Kansas
Format
85 pages
Type
Dissertation
Degree Level
Ph.D.
Discipline
Mathematics
Rights
This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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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.
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- Dissertations [4799]
- Mathematics Dissertations and Theses [179]
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