Related papers: Cut Limits on Hyperbolic Extensions

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…

Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…

We present a statistical approach for the discovery of relationships between mathematical entities that is based on linear regression and deep learning with fully connected artificial neural networks. The strategy is applied to…

We give a concrete description for the boundary of the central quadratic hyperbolic component. The connectedness of the Julia sets of the boundary maps are also considered.

The study of rod complements is motivated by rod packing structures in crystallography. We view them as complements of links comprised of Euclidean geodesics in the 3-torus. Recent work of the second author classifies when such rod…

In this paper, we introduce the concept of quasihyperbolically visible spaces. As a tool, we study the connection between the Gromov boundary and the metric boundary.

Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split reduced non-2-braid prime alternating projections. These links are known to be hyperbolic. Here, we extend to show…

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic…

Let $M$ be a compact hyperbolic $3$-manifold with volume $V$. Let $L$ be a link such that $M\setminus L$ is hyperbolic. For any hyperbolic link $L$ in $M$, in this article, we establish an upper bound of the length of an $n^{th}$ shortest…

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

We set forth a definition of hyperfinite knots. Loosely speaking, these are limits of certain sequences of knots with increasing crossing number. These limits exist in appropriate closures of quotient spaces of knots. We give examples of…

This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with…

This paper is devoted to establishing four types of sharp capacitary inequalities within the hyperbolic space as detailed in Theorems 2.1-3.1-4.1-5.1.

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limit of the value of the ratio of the arithmetic mean of the…

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.

A boundary value problem related to a parabolic higher order operator with a small parameter is analized. When the small parameter tends to zero, the reduced operator is hyperbolic. When t tends to infinity a parabolic hyperbolic boundary…

We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation…

We define finite-time hyperbolic coordinates, describe their geometry, and prove various results on both their convergence as the time scale increases, and on their variation in the state space. Hyperbolic coordinates reframe the classical…