Harmonic mappings and logharmonic functions occupy a central role in complex analysis and applied mathematics. Harmonic mappings are functions that satisfy Laplace’s equation and are frequently ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics.

A continuous function on the complex plane is harmonic if and only if the span of its compositions with entire functions is not dense in the space of continuous functions in the topology of uniform ...

American Journal of Mathematics, Vol. 124, No. 5 (Oct., 2002), pp. 1045-1057 (13 pages) In this paper, we prove the following theorem: Any harmonic functions in Bergman type metrics in the polydisc in ...

The specific topics that will be covered are: the geometry of complex numbers, complex differentiation, Cauchy-Riemann equations, Cauchy's integral theorem and its consequences, Taylor and Laurent ...