Regularity Properties of the Degenerate Monge-Amp`ere Equations on Compact K¨ahler Manifolds

The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact Kǎhler manifolds.     

Regularity Properties of the Degenerate Monge-Amp`ere Equations on Compact K¨ahler Manifolds

The author establishes a result concerning the regularity properties of the degenerate complex Monge-Amp`ere equations on compact K¨ahler manifolds.     

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

Let X be a compact Kähler manifold of dimension k and T be a positive closed current on X of bidimension (p,p) (1≤p<k?1). We construct a continuous linear transform ? _p (T) of T which is a positive closed current on X of bidegree (1,1) which has the same Lelong numbers as T. We deduce from that construction self-intersection inequalities for positive closed currents of any bidegree.     

Regularity Properties of the Degenerate Monge-Ampère Equations on Compact K(a)hler Manifolds

The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact K(a)hler manifolds.