Related papers: A $\Lambda_p$-property for Separated Branches of H…

In their first article, the authors initiated a systematic study of hyperbolic $\Lambda$-metric spaces, where $\Lambda$ is an ordered abelian group, and groups acting on such spaces. The present paper concentrates on the case $\Lambda =…

A finitely generated group is lacunary hyperbolic if one of its asymptotic cones is an $\mathbb{R}$-tree. In this article we give a necessary and sufficient condition on lacunary hyperbolic groups in order to be stable under free product by…

We prove that if the Cayley graph of a finitely generated group enjoys the property L_delta then the group is almost convex and has a sub-cubic isoperimetric function.

Suppose $G$ is a 1-ended finitely generated group that is hyperbolic relative to P a finite collection of 1-ended finitely generated subgroups. Our main theorem states that if the boundary $\partial (G, P)$ has no cut point, then $G$ has…

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

The Sylow p-subgroups of the symmetric group S_p^n satisfy the appropriate generalization of Maschke's Theorem to the case of a p'-group acting on a (not necessarily abelian) p-group. Moreover, some known results about the Sylow p-subgroups…

Let $\mathcal{L}= \partial_t- \Delta_x+|x|^2$. Consider its Poisson semigroup $e^{-y\sqrt{\mathcal{L}}}$. For $\alpha >0$ define the Parabolic Hermite-Zygmund spaces $$ \Lambda^\alpha_{\mathcal{L}}=\left\{f: \:f\in…

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of…

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

A rank $n$ generalized Baumslag-Solitar group is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. In this paper we classify these groups in terms of their separability…

Empirical data on the spectra of light hypernuclei, especially the data from recent gamma-ray experiments, is used to constrain the parameters which govern the p(nucleon)s(Lambda) and p(nucleon)p(Lambda) two-body matrix elements that enter…

In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting. Taking advantage of theses properties, we…

This paper deals with the $L_p$-spectrum of Schr\"odinger operators on the hyperbolic plane. We establish Lieb-Thirring type inequalities for discrete eigenvalues and study their dependence on $p$. Some bounds on individual eigenvalues are…

We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.

Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is…

We consider the periplectic supergroup ${\bf P} (n)$ over a ground field $\Bbbk$ of characteristic $p>2$. We show that there are four blocks of ${\bf P} (n)$ of simple supermodules $L^{\epsilon}(\lambda)$ corresponding to dominant weights…

In this paper we prove a characterization of $p$-hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.

Let $(\Gamma,\mathbb{P})$ be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of $(\Gamma,\mathbb{P})$ is locally connected. Bowditch previously established this conclusion under the additional…

For a transitive sectional-hypebolic set $\Lambda$ with positive volume on a $d$-dimensional manifold $M$($d\ge3$), we show that $\Lambda=M$ and $\Lambda$ is a uniformly hyperbolic set without singularities

The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…