A counterexample concerning the maximum and minimum of a subharmonic function

Fryntov, Alexander

doi:10.1090/S0002-9939-1994-1189746-5

A counterexample concerning the maximum and minimum of a subharmonic function
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by Alexander Fryntov PDF

Proc. Amer. Math. Soc. 122 (1994), 97-103 Request permission

Abstract:

For every $\Delta > 0$ a function u subharmonic in the plane is constructed such that u has the order $\rho = 1 + \Delta$ and satisfies the condition \[ \min \limits _\varphi u(r{e^{i\varphi }})/\max \limits _\varphi u(r{e^{i\varphi }}) \leq - (C + 1)\quad \text {for every} r > 0,\] where $C = C(\rho ) > 0$. This example answers a question of W. K. Hayman.

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