The algebraic surfaces on which the classical Phragmen-Lindelof theorem holds

Let V be an algebraic variety in C-n. We say that V satisfies the strong Phragmen-Lindelof property (SPL) or that the classical Phragmen-Lindelof 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 Cn which satisfy (SPL). Several examples illustrate how these results can be applied.