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/
BYU ScholarsArchive Citation
Boyd, Zachary M., "Convolutions and Convex Combinations of Harmonic Mappings of the Disk" (2014). Theses and Dissertations. 5238.
https://scholarsarchive.byu.edu/etd/5238
Date Submitted
2014-06-01
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd7117
Keywords
geometric function theory, harmonic maps, minimal surfaces, differential geometry
Language
english