Related papers: Kobayashi hyperbolicity of almost complex manifold…

In this article we prove a theorem of Ohsawa-Takegoshi type on compact K\"ahler manifolds. Our arguments follow the "standard" approach for this kind of extension results; however, there are many complications arising from the…

We prove that every bounded strictly $J$-convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We apply this result to the study of the dynamics of pseudo-holomorphic maps.

Applying the Second Main Theorem we deal with the algebraic degeneracy of entire holomorphic curves from the complex plane into a complex algebraic normal variety of positive log Kodaira dimension that admits a finite proper morphism to a…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

A projective manifold is algebraically hyperbolic if the degree of any curve is bounded from above by its genus times a constant, which is independent from the curve. This is a property which follows from Kobayashi hyperbolicity. We prove…

We introduce a new approach to the geometric Bombieri--Lang conjecture for hyperbolic varieties in characteristic 0. The main idea is to construct an entire curve on a special fiber of a variety over a complex function field from an…

We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…

Brady proved that there are hyperbolic groups with finitely presented subgroups that are not of type $FP_3$ (and hence not hyperbolic). We reprove Brady's theorem by presenting a new construction. Our construction uses Bestvina-Brady Morse…

We give a generalization of the nonexistence of level structures as Nadel, Noguchi, Hwang-To, for quasi-projective manifolds uniformized by strongly Carath\'eodory hyperbolic complex manifolds. Examples include moduli space of compact…

In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira…

We prove the existence of a leaf, which is injective Brody in $\mathbb{P}^2$, in the foliation of the boundary of the set of non-escaping points for certain H\'enon mappings.

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a "hyperbolic non-percolation" property. We use this method to show that general small deformations of…

We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…

We discuss an example related to the method of Brody. The example is an open subset of a compact complex torus which is covered by entire curves, but not by Brody curves.

We introduce two notions of hyperbolicity for not necessarily K\"ahler even balanced $n$-dimensional compact complex manifolds $X$. The first, called {\it SKT hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of SKT…

The main result is a short effective proof of Tao Li's theorem that a closed non Haken hyperbolic 3-manifold N has at most finitely many irreducible Heegaard splittings.

Complete hyperbolicity of small Euclidean balls with respect to a C^1-smooth almost complex structure standard at origin is improved to give a complete hyperbolicity of strictly pseudoconvex domains. More precise (and lower) regularity…

We construct families of convex domains that are biholomorphic to bounded domains, but not bounded convex domains. This is accomplished by finding an obstruction related to the Gromov hyperbolicity of the Kobayashi metric.

We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of…

This note proves orbifold versions of Kobayashi's theorem. The main result asserts that a compact K\"ahler orbifold with non-negative Ricci curvature, along with certain conditions regarding singularities, is simply connected.