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Convolutions and Convex Combinations of Harmonic Mappings of the Disk

Let f_1, f_2 be univalent harmonic mappings of some planar domain D into the complex plane C. This thesis contains results concerning conditions under which the convolution f_1 ∗ f_2 or the convex combination tf_1 + (1 − t)f_2 is univalent. This is a long-standing problem, and I provide several partial solutions. I also include applications to minimal surfaces.

Identiferoai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-6237
Date01 June 2014
CreatorsBoyd, Zachary M
PublisherBYU ScholarsArchive
Source SetsBrigham Young University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations
Rightshttp://lib.byu.edu/about/copyright/

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