Abstract

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.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2014-06-01

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd7117

Language

english

Included in

Mathematics Commons

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