Conformal Duality and Compact Complex Surfaces.
Let L(z) be the Lie norm on and L*(z) the dual Lie norm. We denote by the space of complex harmonic functions on the open Lie ball and by the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.
In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...
We prove that the Carathéodory discs for doubly connected domains in the complex plane are connected.
In this paper we construct non-trivial examples of blow-analytic isomorphisms and we obtain, via toric modifications, an inverse function theorem in this category. We also show that any analytic curve in , can be deformed via a rational blow- analytic isomorphism of , to a smooth analytic arc.
Étant donné un ensemble analytique de codimension dans , nous construisons des hypersurfaces irréductibles de lieu singulier , avec contrôle de la croissance. À partir d’un contre-exemple au problème de Bezout transcendant, dû à M. Cornalba et B. Shiffman, nous montrons l’existence d’une courbe irréductible d’ordre 0 dans , dont le lieu singulier est d’ordre infini. Nous étudions également en application certaines propriétés arithmétiques de l’anneau de convolution