Envelope of Dirichlet problems on a domain in
Equidistribution towards the Green current for holomorphic maps
Let be a non-invertible holomorphic endomorphism of a projective space and its iterate of order . We prove that the pull-back by of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to when tends to infinity. We also give an analogous result for the pull-back of positive closed -currents and a similar result for regular polynomial automorphisms of .
Estimates of the Bergman kernel function on certain pseudoconvex domains in Cn.
Estimations pour l’opérateur d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète
Existence and approximation Theorems on a Weakly 1-Complete Analytic Space.
Extension and lacunas of solutions of linear partial differential equations
Let be compact, convex sets in with and let be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of in the space of all -functions on extends to a zero solution in resp. in . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of in and in terms of fundamental solutions for with lacunas.
Extension of Positive Line Bundles and Meromorphic Maps.
Extremal plurisubharmonic functions
We study different notions of extremal plurisubharmonic functions.
Extremal plurisubharmonic functions and invariant pseudodistances
Extremal plurisubharmonic functions in
Extremal plurisubharmonic functions of linear growth on algebraic varieties.
Extreme plurisubharmonic singularities
A plurisubharmonic singularity is extreme if it cannot be represented as the sum of non-homothetic singularities. A complete characterization of such singularities is given for the case of homogeneous singularities (in particular, those determined by generic holomorphic mappings) in terms of decomposability of certain convex sets in ℝⁿ. Another class of extreme singularities is presented by means of a notion of relative type.
Finitely generated ideals in
The Gleason problem is solved on real analytic pseudoconvex domains in . In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are -points as studied by Range and therefore allow local sup-norm estimates for .
Foliations by complex manifolds involving the complex Hessian [Book]
Fonction de Green pluriclomplexe à pole à l'infini sur un espace de Stein parabolique et applications.
Fonctions analytiques et fonctions plurisousharmoniques dans les espaces vectoriels topologiques
Fundamental solutions of the complex Monge-Ampère equation
We prove that any positive function on ℂℙ¹ which is constant outside a countable -set is the order function of a fundamental solution of the complex Monge-Ampère equation on the unit ball in ℂ² with a singularity at the origin.
Geodesic Convexity and Plurisubharmonicity on Hermitian Manifolds.
Geometry and cohomology of certain domains in the complex projective space.
Growth properties of analytic and plurisubharmonic functions of finite order.