Related papers: Solutions a divers problemes de decision dans un g…

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.

We consider the ultrahyperbolic equation in the Euclidean space. The behavior at the infinity of a certain class of solutions is studied. We examine the issue of existence of solutions to the scattering problem: for a given asymptotics at…

We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth.

This work is concerned with the stable norm in word hyperbolic groups as defined by Gromov. We give a short elementary proof of one of its basic property, that is existence of a computable uniform non null lower bound for stable norm in a…

An introduction to Hyperbolic Analysis is presented.

We give a complete classification of complex hyperbolic $(n_1, n_2, n_3)$-triangle groups by types defined according to the ellipticity of two particular words of short length. This improves the Schwartz conjecture proved by Grossi.

In this paper we study the generic, i.e., typical, behavior of finitely generated subgroups of hyperbolic groups and also the generic behavior of the word problem for amenable groups. We show that a random set of elements of a nonelementary…

In this paper we improve the approach of a previous paper about the domino problem in the hyperbolic plane, see arXiv.cs.CG/0603093. This time, we prove that the general problem of the hyperbolic plane with \`a la Wang tiles is undecidable.

In this paper we study the word problem of groups corresponding to tessellations of the hyperbolic plane. In particular using the Fibonacci technology developed by the second author we show that groups corresponding to the pentagrid or the…

We choose random points in the hyperbolic disc and claim that these points are already word representations. However, it is yet to be uncovered which point corresponds to which word of the human language of interest. This correspondence can…

We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutions sets of quadratic equations in a free group.

We provide infinitely many solutions of a Dirichlet problem on balls.

Lower bounds for some explicit decision problems over the complex numbers are given.

Let $G$ be an acylindrically hyperbolic group and $E$ an exponential equation over $G$. We show that if $E$ is solvable in $G$, then there exists a solution whose components, corresponding to loxodromic elements, can be linearly estimated…

We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We show that a group that is hyperbolic relative to strongly shortcut groups is itself strongly shortcut, thus obtaining new examples of strongly shortcut groups. The proof relies on a result of independent interest: we show that every…

The aim of this short note is to provide a proof of the decidability of the generalized membership problem for relatively quasi-convex subgroups of finitely presented relatively hyperbolic groups, under some reasonably mild conditions on…

We give necessary and sufficient conditions for a hyperbolic set to be non-chaotic (or, conversely, chaotic) in a certain sense.

We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these…