Related papers: On Hyperbolicity of Spirallike Circularlike domain

In this paper, we prove that the quasi-projective base of any maximally variational smooth family of Calabi-Yau klt pairs is both of log general type, and pseudo Kobayashi hyperbolic. Moreover, such a base is Brody hyperbolic if the family…

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.…

We give an explicit lower bound, in terms of the distance from the boundary, for the Kobayashi metric of a certain class of bounded pseudoconvex domains in $\mathbb{C}^n$ with $\mathcal{C}^2$-smooth boundary using the regularity theory for…

We show that the base space of a homotopy cofibration is locally hyperbolic under various conditions. In particular, if these manifolds admit a rationally elliptic closure, then almost all punctured manifolds and almost all manifolds with…

We discuss several ways of packing a hyperbolic surface with circles (of either varying radii or all being congruent) or horocycles, and note down some observations related to their symmetries (or the absence thereof).

We show that a general small deformation of the union of two general cones in P3 of degree >= 4 is Kobayashi hyperbolic. Hence we obtain new examples of hyperbolic surfaces in P3 of any given degree d>= 8.

We show that a one-ended simply connected at infinity hyperbolic group $G$ with enough codimension-1 surface subgroups has $\partial G \cong \mathbb{S}^2$. Combined with a result of Markovic, our result gives a new characterization of…

We give an example of a parabolic holomorphic self-map $f$ of the unit ball $\mathbb B^2\subset \mathbb C^2$ whose canonical Kobayashi hyperbolic semi-model is given by an elliptic automorphism of the disc $\mathbb D\subset \mathbb C$,…

It is well-known that billiards in polygons cannot be chaotic (hyperbolic). Particularly Kolmogorov-Sinai entropy of any polygonal billiard is zero. We consider physical polygonal billiards where a moving particle is a hard disc rather than…

Let $S$ be a surface of genus $g$ at least $2$. A representation $\rho:\pi_1S\longrightarrow \text{PSL}_2\Bbb R$ is said to be purely hyperbolic if its image consists only of hyperbolic elements other than the identity. We may wonder under…

In this paper, we investigate the behavior of orbits inside parabolic basins. Let $f(z)=z+az^{m+1}+(\text{higher terms}), m\geq1, a\neq0.$ We choose an arbitrary constant $C>0$ and a point $q\in{\bf v_j}\cap\mathcal{P}_j$. Then there exists…

We construct an elementary counterexample to the criterion for Kobayashi hyperbolicity for a class of tube domains in ${\mathbb C}^2$ proposed by J.-J. Loeb.

We derive geometric formulas for the mass of asymptotically hyperbolic manifolds using coordinate horospheres. As an application, we obtain a new rigidity result of hyperbolic space: if a complete asymptotically hyperbolic manifold has…

In this note, we discuss the following problem: Given a smoothly bounded strongly pseudoconvex domain $D$ in $\mathbb{C}^n$, can we guarantee the existence of geodesics for the Kobayashi--Fuks metric which ``spiral around" in the interior…

We identify as topological spheres those complete submanifolds lying with any codimension in hyperbolic space whose Ricci curvature satisfies a lower bound contingent solely upon the length of the mean curvature vector of the immersion.

We examine Euclidean plane domains with their hyperbolic or quasihyperbolic distance. We prove that the associated metric spaces are quasisymmetrically equivalent if and only if they are bi-Lipschitz equivalent. On the other hand, for…

We study stable immersed capillary hypersurfaces $\Sigma$ in domains B of R n+1 bounded by hyperplanes. When B is a half-space, we show $\Sigma$ is a spherical cap. When B is a domain bounded by k hyperplanes P 1 ,. .. , P k , 2 $\le$ k…

The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.

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 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…