Patrice Assouad, Thierry Quentin de Gromard (2006)
Revista Matemática Iberoamericana
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Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X,d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly
Romain Dujardin (2004)
Publicacions Matemàtiques
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We try to find a geometric interpretation of the wedge product of positive closed laminar currents in C2. We say such a wedge product is geometric if it is given by intersecting the disks filling up the currents. Uniformly laminar currents do always intersect geometrically in this sense. We also introduce a class of strongly approximable laminar currents, natural from the dynamical point of view, and prove that such currents intersect geometrically provided they have continuous potentials. ...
Frédéric Bayart, Augustin Mouze (2005)
Publicacions Matemàtiques
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We discuss some local analytic properties of the ring of Dirichlet series. We obtain mainly the equivalence between the irreducibility in the analytic ring and in the formal one. In the same way we prove that the ring of analytic Dirichlet series is integrally closed in the ring of formal Dirichlet series. Finally we introduce the notion of standard basis in these rings and we give a finitely generated ideal which does not admit standard bases.
Peter Haïssinsky (2005)
Publicacions Matemàtiques
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Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T(X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D= T(X) if and only if the components of X Y are all disks or punctured disks.
Taoufik Hmidi (2006)
Revista Matemática Iberoamericana
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In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is C outside a singular set Σ, so the velocity is, for all time, lipschitzian outside the image of Σ through the viscous flow. In addition, the correponding lipschitzian norm is independent of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex...
Jean-Jacques Loeb (2006)
Publicacions Matemàtiques
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We give several extensions to unbounded domains of the following classical theorem of H. Cartan: A biholomorphism between two bounded complete circular domains of Cn which fixes the origin is a linear map. In our paper, pseudo-convexity plays a main role. Some precise study is done for the case of dimension two and the case where one of the domains is Cn.
Alano Ancona (2007)
Publicacions Matemàtiques
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Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds.
Stéphane Lamy (2005)
Publicacions Matemàtiques
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We describe the structure of the group of algebraic automorphisms of the following surfaces 1) P1,k x P1,k minus a diagonal; 2) P1,k x P1,k minus a fiber. The motivation is to get a new proof of two theorems proven respectively by L. Makar-Limanov and H. Nagao. We also discuss the structure of the semi-group of polynomial proper maps from C2 to C2.
Frédéric Touzet (2003)
Publicacions Matemàtiques
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Using the description of non solvable dynamics by Nakai, we give in this paper a new proof of the rigidity properties of some sub-groups of Diff(C, O). The Cinfinity case is also considered here.
Rafik Meziani, Paulo Sad (2007)
Publicacions Matemàtiques
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This paper presents a classification of plane dicritical nilpotent singularities, i.e. singularities which have nilpotent linear part and infinitely many separatrices. In particular the existence of meromorphic first integrals is discussed. The same ideas are applied to other kind of dicritical singularities.