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The Ahlfors Iteration for Confromal Mapping

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dc.contributor.advisor Bishop, Christopher en_US
dc.contributor.author Green, Christopher Michael en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2013-05-22T17:34:38Z
dc.date.accessioned 2015-04-24T14:45:37Z
dc.date.available 2013-05-22T17:34:38Z
dc.date.available 2015-04-24T14:45:37Z
dc.date.issued 2011-12-01
dc.identifier Green_grad.sunysb_0771E_10740 en_US
dc.identifier.uri http://hdl.handle.net/1951/59670 en_US
dc.identifier.uri http://hdl.handle.net/11401/71026 en_US
dc.description 72 pg. en_US
dc.description.abstract The Riemann Mapping Theorem states that for any proper, simply connected planar domain there exists a conformal mapping from the disk onto the domain. But can this map be explicitly described? For general domains, there is no obvious answer. However, if the domain is the interior of a simple polygon, a convenient formula for the Riemann map was discovered independently by Schwarz and Christoffel. In this dissertation, we present a local quadratically convergent algorithm, the Ahlfors Iteration, based on the theory of quasiconformal maps in the plane, to compute the Schwarz-Christoffel mapping. This algorithm will also apply to a larger collection of simply connected Riemann surfaces. The Ahlfors Iteration improves upon current algorithms that compute the Schwarz-Christoffel map, in that, it is proven to converge, has a simple iterative form, and is easy to implement. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other conformal mappings, quasiconformal mappings, Schwarz-Christoffel formula en_US
dc.title The Ahlfors Iteration for Confromal Mapping en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Milnor, John en_US
dc.contributor.committeemember Simons, James en_US
dc.contributor.committeemember Mullhaupt, Andrew. en_US

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