相关论文: Rigidity for Quasi-M\"obius Actions on Fractal Met…

This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teres\'opolis, Brazil in June 2016. The course introduced a number…

We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in our previous work [5]. In the relatively geometric setting we prove: full relatively…

We make a few observations on the absence of geometric and topological rigidity for acylindrically hyperbolic and relatively hyperbolic groups. In particular, we demonstrate the lack of a well-defined limit set for acylindrical actions on…

We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.

We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such…

This paper studies local rigidity for some isometric toral extensions of partially hyperbolic $\mathbb{Z}^k$ ($k\geqslant 2$) actions on the torus. We prove a $C^\infty$ local rigidity result for such actions, provided that the smooth…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary…

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian…

In 2004, Taubes introduced the space of minimal hyperbolic germs with elements consisting of the first and second fundamental form of an equivariant immersed minimal disk in hyperbolic 3-space. Herein, we initiate a further study of this…

We set up a real entropy function $h_\Bbb{R}$ on the space $\mathcal{M}'_d$ of M\"obius conjugacy classes of real rational maps of degree $d$ by assigning to each class the real entropy of a representative $f\in\Bbb{R}(z)$; namely, the…

Consider a countable group Gamma acting ergodically by measure preserving transformations on a probability space (X,mu), and let R_Gamma be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there…

Suppose G is a hyperbolic group whose boundary has topological dimension k. If the boundary is quasisymmetrically homeomorphic to an Ahlfors k-regular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…

Bowditch characterized relative hyperbolicity in terms of group actions on fine hyperbolic graphs with finitely many edge orbits and finite edge stabilizers. In this paper, we define generalized fine actions on hyperbolic graphs, in which…

We prove that finitely generated amenable groups acting on CAT(0) spaces satisfy the following alternative: either every action on a geodesically complete CAT(0) space with bounded geometry (or finite dimension) has a global fixed point, or…

After a short introduction to the general notion of Borel fields of metric spaces we introduce the notion of the action of an equivalence relation on such fields. Then, we specify the study to the Borel fields of proper CAT(0) spaces and we…

In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…

We compare critical exponent for quasi-Fuchsian groups acting on the hyperbolic 3-space, $\mathbb{H}^3$, and on invariant disks embedded in $\mathbb{H}^3$. We give a rigidity theorem for all embedded surfaces when the action is Fuchsian and…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

We introduce asymptotic-M\"obius (AM) maps, a large-scale analogue of quasi-M\"obius maps tailored to geometric group theory. AM-maps capture coarse cross-ratio behavior for configurations of points that lie far apart, providing a notion of…