Related papers: Worm domains are not Gromov hyperbolic

We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least 3 vertices are not relatively hyperbolic. We then show that the outer automorphism groups are not relatively hyperbolic, if they are not…

It is pointed out that, contrary to some claims in the literature, the domain walls cannot be a source of a correlated at large scales primordial magnetic field, even if the fermionic modes bound on the wall had ferromagnetic properties. In…

We prove that a hyperbolic group cannot contain a strictly ascending chain of free quasiconvex subgroups of constant rank.

A hyperbolic group acts by homeomorphisms on its Gromov boundary. We use a dynamical coding of boundary points to show that such actions are topologically stable in the dynamical sense: any nearby action is semi-conjugate to (and an…

In this paper, we investigate Gromov hyperbolizations of unbounded locally complete and incomplete metric spaces associated with three hyperbolic type metrics: the hyperbolization metric introduced by Ibragimov, the distance ratio metric,…

We study extremal discs for the Kobayashi metric. Inspired by work of Lempert on strongly convex domains, we present results on strongly pseudoconvex domains. We also consider a useful biholomorphic invariant, inspired by the Kobayashi (and…

Given a domain $G \subsetneq \Rn$ we study the quasihyperbolic and the distance ratio metrics of $G$ and their connection to the corresponding metrics of a subdomain $D \subset G$. In each case, distances in the subdomain are always larger…

In this paper, the existence of parabolic boundary points of certain convex domains in $\mathbb C^2$ is given. On the other hand, the nonexistence of parabolic boundary points of infinite type of certain domains in $\mathbb C^2$ is also…

Let $D=\{\rho < 0\}$ be a smooth relatively compact domain in an almost complex manifold $(M,J)$, where $\rho$ is a smooth defining function of $D$, strictly $J$-plurisubharmonic in a neighborhood of the closure $\overline{D}$ of $D$. We…

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We…

We establish a version of a classical theorem of Pommerenke, which is a diameter version of the Gehring-Hayman inequality on Gromov hyperbolic domains of $\mathbb{R}^n$. Two applications are given. Firstly, we generalize Ostrowski's…

We establish constructive geometric tools for determining when a domain is $L^s$-averaging and obtain upper and lower bounds for the $L^s$-integrals of the quasihyperbolic distance. We also construct examples which are helpful to understand…

We show that the graph of a holomorphic motion of the unit disc cannot be biholomorphic to a strongly pseudoconvex domain in C n .

In this note, we introduce the notion of visible boundary points with respect to Kobayashi distance for domains in complex euclidean space. Following the work of Sarkar, we obtain additive and multiplicative localization results about…

We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of the complement of a circle domain. It…

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}…

We survey some recent results and open questions on the approaching geodesics property and its application to the study of the Gromov and horofunction compactifications of a proper geodesic Gromov metric space. We obtain results on the…

We prove that the separating curve graph of a connected, compact, orientable surface with genus at least 3 and a single boundary component is not relatively hyperbolic. This completes the classification of when the separating curve graph is…

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.

In this note, we prove the generic Kobayashi volume measure hyperbolicity of singular directed varieties $(X, V)$, as soon as the canonical sheaf $\mathcal{K}\_V$ of $V$ is big in the sense of Demailly.