A new capacity for plurisubharmonic functions

Relative extremal functions and characterization of pluripolar sets in complex manifolds

“…We begin with a lemma. For similar results see Theorem 8.3 in Bedford and Taylor [3] and Theorem 7.3 in Poletsky [13].…”

“…By Bedford and Taylor [3], Theorem 7.1, the set of all x for which ω(x, A, X) < ω * (x, A, X) is pluripolar in X, so if we know that ω * (·, A, X) = Ω * (·, A, X), then the functions ω(·, A, X) and Ω(·, A, X) are equal outside a pluripolar set.…”

Weak solutions to the complex Hessian equation

“…[1], [2], [5], [11], [18]). The aim of this paper is to concentrate on those problems related to the Hessian operator where the methods of the complex Monge-Ampère operator cannot be automatically repeated.…”

On approximation by special analytic polyhedral pairs

“…The complex Monge-Ampère operator (dd c ) n (see [3]) is defined for any bounded plurisubharmonic function u in D so that (dd c u) n is a non-negative Borel measure on…”

“…In particular, for a pluriregular pair we get a CPT analogue of the equilibrium measure µ 0 (K, Ω) := (dd c ω) n , supported by K (see [3]). …”