Lelong numbers of positive plurisubharmonic currents

Nombre de Lelong directionnel d'un courant positif plurisousharmonique

“…This theorem generalizes a result proved by [1] with ϕ(z) = |z| 2 , v(t) = |t| 2 and B an open ball in L.…”

“…Then by [3] we have j * s (α z ) = j * s (β z )/s. We first prove the following proposition which is a Lelong-Jensen type formula, see [4] and [1].…”

Lelong-Skoda Transform for Compact Kähler Manifolds and Self-Intersection Inequalities

“…That is: if ı : X → X is the blow-up of X at x and T is a cluster value of the sequence ı * (T n ), then the mass of T on the exceptional divisor is equal to the Lelong number ν(T , x) (the proof is exactly the same using formula (6)). Now we define in the same way L p (T ) which is a well defined positive pluriharmonic current of bidegree (1,1). Observe that the arguments of Sect.…”

“…Once again, the Lelong number at a point does not depend on the choice of coordinates (see [1] for the proof in a more general setting of pluriharmonic currents), so we can speak of Lelong numbers on a manifold. Lemma 2.1 still applies for positive pluriharmonic currents.…”

Sur l'existence du nombre de Lelong d'un courant positif psh défini sur une variété presque complexe

“…, z n ) a coordinate system at a such that∂z j = O(|z|) and ∂z j = O(|z|). We use the notation Following calculations made in [3], we have (1,1) .…”