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.
A Wong-Rosay type theorem for proper holomorphic self-maps
In this short paper, we show that the only proper holomorphic self-maps of bounded domains in whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.
Abelian integrals in holomorphic foliations.
The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singularity in the projective space of dimension two. Also we calculate higher Melnikov functions under some...
About the Calabi problem: a finite-dimensional approach
Let us consider a projective manifold and a smooth volume form on . We define the gradient flow associated to the problem of -balanced metrics in the quantum formalism, the -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the -balancing flow converges towards a natural flow in Kähler geometry, the -Kähler flow. We also prove the long time existence of the -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing the...
About the derivatives of Cauchy type integrals in the polydisc.
Abschätzungen für die Anzahl der holomorphen Abbildungen zwischen algebraischen Räumen.
Absolutely isolated singularities of holomorphic vector fileds.
Accelero-summation of the formal solutions of nonlinear difference equations
In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...
A-Codimension and the vanishing topology of discriminants.
Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisousharmoniques
Soit un groupe de Lie complexe et une forme réelle fermée de . Un couple est dit pseudo-convexe, s’il existe sur une fonction régulière, strictement p.s.h., invariante par l’action de et d’exhaustion sur . On dit que est à spectre imaginaire pur, si pour tout de Lie, les valeurs propres de ad sont imaginaires pures. Pour à radical simplement connexe, cette dernière propriété équivaut à la pseudo-convexité de . Pour pseudo-convexe et sous une hypothèse de sous-groupe discret,...