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We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds. [ABSTRACT FROM AUTHOR]

Given an integer 1 ≤ p ≤ n − 1, we consider a plurisubharmonic positive currentTof bidimension (p, p) on an open subset of ℂncontaining the origin. The tangent cone toTat the origin, if it exists, is the weak limit of dilations ofTby homotheties. Even when the tangent cone fails to exist, every weak limit at 0 of a subsequence of dilations ofTis a positive, plurisubharmonic conical current on ℂnwith the same Lelong number at the origin asT. We give a sufficient condition, in terms of estimates of the mass of the trace measure, for the existence of the tangent cone. [ABSTRACT FROM AUTHOR]

We prove the existence of a maximal plurisubharmonic minorant of a given upper semicontinous function f on an almost complex manifold (M, J) of complex dimension two. Such maximal function is obtained as the pointwise minimum of averages offover the boundaries of all J-complex discs in M centered at the given point. This result is an almost complex analogue of classical results of Poletsky, Larusson and Sigurdsson, Rosay and others in the case when the almost complex structure J is integrable. [ABSTRACT FROM PUBLISHER]