The algebraic surfaces on which the classical Phragmén-Lindelöf theorem holds

Abstract

Let V be an algebraic variety in . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by | z |+ o (| z |) on V and by 0 on the real points in V already is bounded by A | Im z |. For algebraic varieties V of pure dimension k we derive necessary conditions on V to satisfy (SPL) and we characterize the curves and surfaces in which satisfy (SPL). Several examples illustrate how these results can be applied.