Harmonic univalent mappings are complex functions defined on the open unit disk that satisfy Laplace’s equation and exhibit a one-to-one correspondence between the domain and their image. These ...
Certain elements of the boundary dependence of minimal harmonic functions in Euclidean domains are considered. For a given minimal harmonic function $h$ on a domain ...
In this note we show that if the areal mean-value theorem holds for a plane domain (subject to a mild regularity condition) for all integrable harmonic functions, then the domain must be a disk. It is ...
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