Quasiconformal mappings in the complex plane

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dc.contributor.advisor Stankewitz, Richard L. en_US
dc.contributor.author Mercer, Nathan T. en_US
dc.date.accessioned 2011-06-03T19:41:03Z
dc.date.available 2011-06-03T19:41:03Z
dc.date.created 2006 en_US
dc.date.issued 2006
dc.identifier LD2489.Z78 2006 .M47 en_US
dc.identifier.uri http://cardinalscholar.bsu.edu/handle/handle/188151
dc.description.abstract It is well known that, as a consequence of the Identity Theorem, we cannot "glue" together two analytic functions to create a new globally analytic function. In this paper we will both introduce and investigate special homeomorphisms, called quasiconformal maps, that are generalizations of the well known conformal maps. We will show that quasiconformal maps make this "gluing," up to conjugation, possible. Quasiconformal maps are a valuable tool in the field of complex dynamics. We will see how quasiconformal maps of infinitesimal circles have an image of an infinitesimal ellipse. Although quasiconformal maps are nice homeomorphisms, they might only be differentiable in the real sense almost everywhere and, surprisingly, complex differentiable nowhere. We shall rely on the work of Lehto and Virtanen as well as Shishikura in exploring these interesting complex valued functions.
dc.description.sponsorship Department of Mathematical Sciences
dc.format.extent 77 leaves : ill. ; 28 cm. en_US
dc.source Virtual Press en_US
dc.subject.lcsh Quasiconformal mappings. en_US
dc.subject.lcsh Functions of complex variables. en_US
dc.title Quasiconformal mappings in the complex plane en_US
dc.description.degree Thesis (M.S.)
dc.identifier.cardcat-url http://liblink.bsu.edu/catkey/1348866 en_US

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  • Master's Theses [5510]
    Master's theses submitted to the Graduate School by Ball State University master's degree candidates in partial fulfillment of degree requirements.

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