In a differential geometry setting, we can analyze the solutions to systems of differential equations in such a way as to allow us to derive entire classes of solutions from any given solution. This process involves calculating the Lie symmetries of a system of equations and looking at the resulting transformations. In this paper we will give a general background of the theory necessary to develop the ideas of working in the jet space of a given system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with constant Jacobian, harmonic functions with fixed convexity and a few other subclasses of harmonic functions.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Petersen, Willis L., "The Lie Symmetries of a Few Classes of Harmonic Functions" (2005). Theses and Dissertations. 316.
Lie symmetries, harmonic functions, area preserving, Lie group, geometric function theory, schlicht functions, differential geometry, manifolds, Lie algebra