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 ...

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 ...

These functions, which are characterised by their upper semi-continuity and subharmonicity along complex lines, are instrumental in formulating and solving complex Monge-Ampère equations.