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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Boyd, Zachary M., "Convolutions and Convex Combinations of Harmonic Mappings of the Disk" (2014). Theses and Dissertations. 5238.