The Bergman projection on harmonic functions
The Bloch Space of M-Harmonic Functions on Bounded Symmetric Domains.
The Bremermann-Dirichlet problem for -plurisubharmonic functions
The complex Monge-Ampère operator in hyperconvex domains
The Dirchlet Problem for a Complex Monge-Ampère Equation.
The Intersection of the Closures of Two Disjoint Strongly Pseudoconvex Domains.
The Partial Legendre Transformation for Plurisubharmonic Functions.
The restriction theorem for fully nonlinear subequations
Let be a submanifold of a manifold . We address the question: When do viscosity subsolutions of a fully nonlinear PDE on , restrict to be viscosity subsolutions of the restricted subequation on ? This is not always true, and conditions are required. We first prove a basic result which, in theory, can be applied to any subequation. Then two definitive results are obtained. The first applies to any “geometrically defined” subequation, and the second to any subequation which can be transformed...
The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol
Hörmander has characterized the surjective constant coefficient partial differential operators on the space of all real analytic functions on by a Phragmén-Lindelöf condition. Geometric implications of this condition and, for homogeneous operators, of the corresponding condition for Gevrey classes are given.
The symmetric pluricomplex Green function
Topologies semi-vectorielles. Application à l'analyse complexe
On définit sur un espace vectoriel une classe de topologies qui rendent la multiplication continue, mais ne sont pas vectorielles en général. Sur un espace complexe elles permettent d’obtenir encore les principales propriétés des fonctions plurisousharmoniques. De telles topologies séparées sont localement pseudo-convexes (mais non localement convexes en général) : cette notion intervient dans les extensions données récemment par l’auteur du théorème de Banach-Steinhaus aux familles de polynômes...
Traces of pluriharmonic functions
Traces of pluriharmonic functions on the boundaries of analytic varieties.