Related papers: Local Rigidity of Partially Hyperbolic Actions

We study slow entropy invariants for abelian unipotent actions $U$ on any finite volume homogeneous space $G/\Gamma$. For every such action we show that the topological slow entropy can be computed directly from the dimension of a special…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $\mu$, random walks with…

Let $G$ be a group acting $2$-transitively on the boundary of a locally finite tree, and exclude the situation (which is a genuine exception) where $G$ has both $\mathrm{P}\Gamma\mathrm{L}_3(4)$ and $\mathrm{P}\Gamma\mathrm{L}_3(5)$ as…

We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…

We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result concerning abelian groups of…

In this paper, we show that hyperbolic groups admit proper affine isometric actions on $l^p$-spaces.

We study hyperpolar actions on reducible symmetric spaces of the compact type. Our main result is that an indecomposable hyperpolar action on a symmetric space of the compact type is orbit equivalent to a Hermann action or of cohomogeneity…

This paper contains some more results on the topology of a nondegenerate action of $\mathbb{R}^n$ on a compact connected $n$-manifold $M$ when the action is totally hyperbolic (i.e. its toric degree is zero). We study the…

We classify the effective and transitive actions of a Lie group $G$ on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that $G$ is a closed, connected Lie subgroup of…

For a two-dimensional Artin group $A$ whose associated Coxeter group is hyperbolic, we prove that the action of $A$ on the hyperbolic space obtained by coning off certain subcomplexes of its modified Deligne complex is acylindrical.…

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces of dimension greater than two. For the quaternionic…

We consider two manifestations of non-positive curvature: acylindrical actions on hyperbolic spaces and quasigeodesic stability. We study these properties for the class of hierarchically hyperbolic groups, which is a general framework for…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of…

Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and…

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space,…

We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

In this paper, we show local smooth rigidity for higher rank ergodic nilpotent action by toral automorphisms and prove the existence of such action on any torus TN for any even N ? 6. We also give examples of smooth rigidity of actions…

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic $\mathbb{Z}^d$-actions given by Schmidt using…