The Bremermann-Dirichlet problem for -plurisubharmonic functions
The comparison principle and Dirichlet problem in the class , p > 0
We establish the comparison principle in the class . The result obtained is applied to the Dirichlet problem in .
The Dirichlet problem for the degenerate Monge-Ampère equation.
Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that:det (uij) = 0 in Ωu = φ given on ∂Ω.
The generalized three circle- and other convexity theorems with application to the construction of envelopes of holomorphy
The geometry of some natural conjugacies in dynamics.
The gradient lemma
We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
The Intersection of the Closures of Two Disjoint Strongly Pseudoconvex Domains.
The Levi problem in Stein spaces.
The Levi Problem on Complex Spaces with Singularities.
The logarithmic capacity in
The non-pluripolarity of compact sets in complex spaces and the property for the space of germs of holomorphic functions
The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property for the dual space of the space of germs of holomorphic functions on that compact set.
The Partial Legendre Transformation for Plurisubharmonic Functions.
The pluricomplex Green function on some regular pseudoconvex domains
Let D be a smooth bounded pseudoconvex domain in ℂⁿ of finite type. We prove an estimate on the pluricomplex Green function of D that gives quantitative information on how fast the Green function vanishes if the pole w approaches the boundary. Also the Hölder continuity of the Green function is discussed.
The ratio of invariant metrics on the annulus and theta 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 Serre Problem on Riemann Surfaces.
The symmetric pluricomplex Green function
The use of conjugate convex functions in complex analysis
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