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.
| Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-6237 |
| Date | 01 June 2014 |
| Creators | Boyd, Zachary M |
| Publisher | BYU ScholarsArchive |
| Source Sets | Brigham Young University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | http://lib.byu.edu/about/copyright/ |
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