Holomorphic mapping of annuli in and the associated extremal function
Holomorphic mappings between algebraic hypersurfaces in complex space
Holomorphic mappings between spaces of different dimensions. I.
Holomorphic Mappings from the Ball and Polydisc.
Holomorphic Mappings in the Nevanlinna Class.
Holomorphic maps form the unit ball of CN that take hyperplanes into hyperplanes.
Holomorphic Maps of Compact Riemann Surfaces Into 2-Dimensional Compact C-Hyperbolic Manifolds.
Holomorphic submersions from Stein manifolds
We establish the homotopy classification of holomorphic submersions from Stein manifolds to Complex manifolds satisfying an analytic property introduced in the paper. The result is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.
Horospheres and Iterates of Holomorphic Maps.
How to prove Fefferman's theorem without use of differential geometry
Hyperbolic measure of maximal entropy for generic rational maps of
Let be a dominant rational map of such that there exists with for all . Under mild hypotheses, we show that, for outside a pluripolar set of , the map admits a hyperbolic measure of maximal entropy with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of to . This provides many examples where non uniform hyperbolic dynamics is established.One of the key tools is to approximate the graph of a meromorphic...
Hyperbolically Imbedded Spaces and the Big Picard Theorem.
Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties
The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety
Hyperbolic-like manifolds, geometrical properties and holomorphic mappings
The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.
Image of analytic hypersurfaces. II.
Injective endomorphisms of algebraic and analytic sets
We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.
Integrals for holomorphic foliations with singularities having all leaves compact
We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.
Integrated density of states of self-similar Sturm–Liouville operators and holomorphic dynamics in higher dimension
Intrinsic measures complex manifolds
Intrinsic pseudo-volume forms for logarithmic pairs
We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic -correspondences. We define an intrinsic logarithmic pseudo-volume form for every pair consisting of a complex manifold and a normal crossing Weil divisor on , the positive part of which is reduced. We then prove that is generically non-degenerate when is projective and ...