Harmonic majorization of a subharmonic function on a cone or on a cylinder (Q1175128)

The author generalizes the classical Phragmén-Lindelöf theorem for a subharmonic function \(u\) defined on a cone or a cylinder and bounded on the boundary by a certain function. The results are essentially based on the author's previous paper [Proc. Lond. Math. Soc., III. Ser. 54, 267- 299 (1987; Zbl 0645.31003)]. The crucial idea is to find a harmonic majorant of \(u\) and verify in the case \(u\) is non-negative that this harmonic majorant is the least harmonic majorant. The author also considers some applications of these results for the classical Dirichlet problem on a cone or cylinder.