相关论文: Hyperbolic surfaces in ${\bf P}^3$: examples

We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.

Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…

We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…

We provide a geometric condition ensuring that a very general element of a complete linear system on an abelian variety is Kobayashi hyperbolic. Some related conjectures are also given.

In this paper we study the global geometry of the Kobayashi metric on domains in complex Euclidean space. We are particularly interested in developing necessary and sufficient conditions for the Kobayashi metric to be Gromov hyperbolic. For…

In this paper we determine all Kobayashi-hyperbolic 2-dimensional complex manifolds for which the group of holomorphic automorphisms has dimension 3. This work concludes a recent series of papers by the author on the classification of…

We construct a weakly complete flat surface in hyperbolic 3-space having a pair of hyperbolic Gauss maps both of whose images are contained in an arbitrarily given open disc in the ideal boundary of H^3. This construction is accomplished as…

We give two new elementary proofs of the complete Kobayashi hyperbolicity of the twice-punctured complex plane. We also present an extremely short proof that bounded domains are complete Kobayashi hyperbolic. Our proofs rely neither on the…

There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…

Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…

For a geometrically finite hyperbolic surface of infinite volume we write down the spectral decomposition for the Laplacian on 1-forms, generalize the Kudla and Millson's construction of hyperbolic Eisenstein series and other related…

For any H in [0,1), we construct complete, non-proper, stable, simply-connected surfaces with constant mean curvature H embedded in hyperbolic 3-space.

We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…

We give a construction that connects the Cauchy problem for Liouville elliptic equation with a certain initial value problem for mean curvature one surfaces in hyperbolic 3-space H3, and solve both of them. We construct the only mean…

We consider the problem of when a closed orientable hyperbolic surface admits a totally geodesic embedding into a closed orientable hyperbolic 3-manifold; given a finite isometric group action on the surface, we consider in particular…

The Green--Griffiths--Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and…

This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in $\mathbb{P}^3$ of degree at least $17$ is Kobayashi hyperbolic. -- The complement of a {\em generic}…

This is essentially a survey paper in which we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of hyperfunctions. Besides the classical Cauchy-Kowalevsky…

In this paper we prove that every quasi-projective base space $V$ of smooth family of minimal projective manifolds with maximal variation is pseudo Kobayashi hyperbolic, i.e. $V$ is Kobayashi hyperbolic modulo a proper subvariety…

We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage of the extended real line under the projection map is…