Algebraic varieties on which the classical Phragmen-Lindelof estimates hold for plurisubharmonic functions

Algebraic varieties V are investigated on which the natural analogue of the classical Phragmen-Lindelof principle for plurisubharmonic functions holds . For a homogeneous polynomial P in three variables it is shown that its gr aph has this property if and only if P has real coefficients, no elliptic f actors, is locally hyperbolic in all real characteristics, and the localiza tions in these characteristics are square-free, The last condition is shown to be necessary in any dimension.