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math.CV2020
On a result of Hayman concerning the maximum modulus set
Vasiliki Evdoridou, Leticia Pardo-Simón, David J. Sixsmith
The set of points where an entire function achieves its maximum modulus is known as the maximum modulus set. In 1951, Hayman studied the structure of this set near the origin. Foll…
math.CV2020
The maximum modulus set of a quasiregular map
Alastair N. Fletcher, David J. Sixsmith
We study, for the first time, the maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point of each modulu…
math.DS2020
Fatou's associates
Vasiliki Evdoridou, Lasse Rempe, David J. Sixsmith
Suppose that is a transcendental entire function, is a simply connected domain, and is a connected component of . Using Riemann maps, w…