Related papers: Hyperbolic Extensions and Metrics $\epsilon$-Close…

We define and study "hyperbolic forcing".

We study the relationship between two concepts: cut limits and hyperbolic extensions.

We define and study "warp forcing".

An introduction to Hyperbolic Analysis is presented.

The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.

We survey the known results regarding the boundaries of word-hyperbolic groups.

Consider a finitely generated group $G$ that is relatively hyperbolic with respect to a family of subgroups $H_1, ..., H_n$. We present an axiomatic approach to the problem of extending metric properties from the subgroups $H_i$ to the full…

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…

We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…

We study the growth of hyperbolic type distances in starlike domains. We derive estimates for various hyperbolic type distances and consider the asymptotic sharpness of the estimates.

We mainly consider two metrics: a Gromov hyperbolic metric and a scale invariant Cassinian metric. We compare these two metrics and obtain their relationship with certain well-known hyperbolic-type metrics, leading to several inclusion…

An alternative method is described for determining the hyperbolic structure on a link complement, and some of its elementary consequences are examined. The method is particularly suited to alternating links.

Localization and dilation procedures are discussed for infinite dimensional $\alpha$-concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measures).

The density of the hyperbolic metric on the complement of a rectangular lattice is investigated. The question is related to conformal mapping of symmetric circular quadrilaterals with all zero angles.

We explain how to construct certain potential functions for the hyperbolic structures of a knot complement, which are closely related to the analytic functions on the deformation space of hyperbolic structures.

We survey several methods of extending quasisymmetric homeomorphisms of the real line to bi-Lipschitz diffeomorphisms of the upper half-plane with respect to the hyperbolic metric.

We find the explicit local models of isolated singularities of conformal hyperbolic metrics by Complex Analysis, which is interesting in its own and could potentially be extended to high-dimensional case.

Formal languages based on the multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.

We study those group rings whose group of units is hyperbolic.

Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…