A Theorem of Versality for Unfoldings of Complex Analytic Foliation Singularities.
A theorem on complete intersection curves and a consequence for the runge problem for analytic sets
A Theorem on Solutions of Analytic Equations with Applications to Deformations of Complex Structures.
A Topological Criterion for Local Optimality of Weakly Normal Complex Spaces.
A topological resolution theorem
A triple ratio on the Silov boundary of a bounded symmetric domain
Let be a Hermitian symmetric space of tube type, its Silov boundary and the neutral component of the group of bi-holomorphic diffeomorphisms of . Our main interest is in studying the action of on . Sections 1 and 2 are part of a joint work with B. Ørsted (see [4]). In Section 1, as a pedagogical introduction, we study the case where is the unit disc and is the circle. This is a fairly elementary and explicit case, where one can easily get a flavour of the more general results. In Section...
A Twistor Correspondence for Homogeneous Polynomial Differential Operators.
A unicity theorem for plurisubharmonic functions
We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
A unified approach to the theory of separately holomorphic mappings
We extend the theory of separately holomorphic mappings between complex analytic spaces. Our method is based on Poletsky theory of discs, Rosay theorem on holomorphic discs and our recent joint-work with Pflug on boundary cross theorems in dimension It also relies on our new technique of conformal mappings and a generalization of Siciak’s relative extremal function. Our approach illustrates the unified character: “From local information to global extensions”. Moreover, it avoids systematically...
A uniqueness property for measures on
A uniqueness theorem for invariantly harmonic functions in the unit ball of Cn.
We prove a boundary uniqueness theorem for harmonic functions with respect to Bergman metric in the unit ball of Cn and give an application to a Runge type approximation theorem for such functions.
A uniqueness theorem of Cartan-Gutzmer type for holomorphic mappings in ℂⁿ
We continue our previous work on a problem of Janiec connected with a uniqueness theorem, of Cartan-Gutzmer type, for holomorphic mappings in ℂⁿ. To solve this problem we apply properties of (j;k)-symmetrical functions.
A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles.
A Vanishing Theorem for Power Series.
A vanishing theorem on arithmetic surfaces.
A variational characterization of condenser capacities in within a class of plurisubharmonic functions
A viscosity approach to degenerate complex Monge-Ampère equations
This is the content of the lectures given by the author at the winter school KAWA3 held at the University of Barcelona in 2012 from January 30 to February 3. The main goal was to give an account of viscosity techniques and to apply them to degenerate Complex Monge-Ampère equations.We will survey the main techniques used in the viscosity approach and show how to adapt them to degenerate complex Monge-Ampère equations. The heart of the matter in this approach is the “Comparison Principle" which allows...
A weak invertibility criterion in the weighted -spaces of holomorphic functions in the ball.
A weighted Plancherel formula II. The case of the ball
The group SU(1,d) acts naturally on the Hilbert space , where B is the unit ball of and the weighted measure . It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic...
A weighted Plancherel formula. III. The case of the hyperbolic matrix ball.