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This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
Abstract: Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subg...
Abstract: We construct and classify all groups acting simply transitively on vertices of hyperbolic triangular buildings of the smallest non-trivial thickness. We have both torsion and torsion free gr...
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff source term. On one hand, we determine the relevant asymptotic expa...
We study minimal immersions of closed surfaces (of genus $g \ge 2$) in hyperbolic 3-manifolds, with prescribed data $(\sigma, t\alpha)$, where $\sigma$ is a conformal structure on a topological surfac...
This paper is a continuation of our paper about boundary rigidity and filling minimality of metrics close to flat ones. We show that compact regions close to a hyperbolic one are boundary distance rig...
We study those group rings whose group of units is hyperbolic.Let (X, ) be a metric space with metric . For any a, b, c ∈ X, the Gromov product hb, cia of b and c with respect to a ∈ X is defined as...
The K-theoretic analog of Spanier-Whitehead duality for noncommutative C-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces.This had previously been proved only ...
In this paper, the Dirac operator on the Klein model for the hyperbolic space is considered. A function space containing $L_2$-functions on the sphere $S^{m-1}$ in $\mR^m$ which are boundary values of...
We consider the Cauchy problem ${\varepsilon}{u_{\ep}}''+\delta{u_{\ep}}'+A{u_{\varepsilon}}=0,$ ${u_{\varepsilon}}(0)=u_0, $ ${u_{\varepsilon}}'(0)=u_{1},$ where ${\varepsilon}>0$, $\delta>0$, $H$ is...
摘要 In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary and sufficient condition for Cartan matric...
The equation L(u):=k(y)uxx-\partialy(\ell(y)uy)+r(x,y)u=f(x,y,u), where k(y)>0, \ell(y)>0 for y>0,k(0)=\ell(0)=0 and limy\rightarrow 0k(y)/\ell(y) exists, is strictly hyperbolic for y>0 and its order ...

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