An elliptic second main theorem
We prove a second main theorem for elliptic projective planes.
math.CV↗
arXiv subjects
Julien Duval
Publications and source records attributed to Julien Duval.
Polynomial hull of a torus fibered over the circle
Given a 2-sheeted torus over the circle with winding number 1, we prove that its polynomial hull is a union of 2-sheeted holomorphic discs. Moreover when the hull is non degenerate its boundary is a Levi-flat solid torus foliated by such discs.
math.CV↗
Singularities of local Ahlfors currents
We prove that a complex curve charged by a local Ahlfors current is either a disc or an annulus.
math.CV↗
A geometric second main theorem
We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.
math.CV↗
On a result by Y. Groman and J. P. Solomon
We give a short proof of a reverse isoperimetric inequality due to Y. Groman and J. P. Solomon.
math.CV↗
Sur la théorie d'Ahlfors des surfaces
We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.
math.CV↗
Sur les courbes de Brody dans P^n(C)
We investigate Brody curves in the projective space from the point of view of Nevanlinna theory.
math.CV↗
Riemann surfaces and totally real tori
Given a generic totally real torus unknotted in the unit sphere of the complex plane, we prove the following alternative : either there exists a filling of the torus by holomorphic discs and the torus is rationally convex, or its rational hull contains a holomorphic annulus.
math.CV↗
Sur le lemme de Brody
Brody's lemma is a basic tool in complex hyperbolicity. We present a version of it making more precise the localization of an entire curve coming from a diverging sequence of holomorphic discs. As a byproduct we characterize hyperbolicity in terms of an isoperimetric inequality.
math.CV↗
Singularites des courants d'Ahlfors
We prove that an algebraic curve charged by a current coming from an entire curve is rational or elliptic. This answers a question by M. Paun.
math.CV↗
Un theoreme de Green presque complexe
We prove the hyperbolicity of the complement of five lines in general position in an almost complex projective plane, answering a question by S. Ivashkovich.
math.CV↗
Deux caracterisations de la mesure d'equilibre d'un endomorphisme de Pk(C)
Let $μ$ be the equilibrium measure of an endomorphism of ${\sf P}^k({\bf C})$. We show that it is its unique measure of maximal entropy. We build $μ$ directly as the distribution of any point outside an algebraic exceptional set.
math.DS↗