Related papers: Conformal graph directed Markov systems on Carnot …

We study skew-product dynamics for a large class of finitely-generated semi--hyperbolic semigroups of rational maps acting on the Riemann sphere, which generalizes both the theory of iteration of a single rational map of a single complex…

Let Gamma be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin-Razborov diagrams for Gamma. We also prove that every system of equations over Gamma is equivalent to a finite…

We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…

In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…

The notion of curvature discussed in this paper is a far going generalization of the Riemannian sectional curvature. It was first introduced by Agrachev, Barilari and Rizzi in arXiv:1306.5318, and it is defined for a wide class of optimal…

The main result of the present paper is a Rademacher-type theorem for intrinsic Lipschitz graphs of codimension $k\leq n$ in sub-Riemannian Heisenberg groups $\mathbb H^n$. For the purpose of proving such a result we settle several related…

We construct Markov partitions for non-invertible and/or singular nonuniformly hyperbolic systems defined on higher dimensional Riemannian manifolds. The generality of the setup covers classical examples not treated so far, such as geodesic…

We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher diffusion driven algorithm and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the…

Perhaps the fundamental theorem of geometric group theory, the Milnor--Schwarz lemma gives conditions under which the orbit map relating the geometry of a geodesic metric space and the word metric on a group acting isometrically on the…

In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…

To reinforce the analogy between the mapping class group and the Cremona group of rank $2$ over an algebraic closed field, we look for a graph analoguous to the curve graph and such that the Cremona group acts on it non-trivially. A…

We formalize the notion of limit of an inverse system of metric spaces with $1$-Lipschitz projections having unbounded fibers. The purpose is to use sub-Riemannian groups for metrizing the space of signatures of rectifiable paths in…

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…

An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carath\'eodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the…

We provide a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that we show is canonically available, given a choice of complement to the distribution. We also describe conditions…

We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a finitely generated free group.

The purpose of this paper is to provide a uniformization procedure for Gromov hyperbolic spaces, which need not be geodesic or proper. We prove that the conformal deformation of a Gromov hyperbolic space is a bounded uniform space. Further,…

We develop a homotopy theory of directed graphs based on cubical homotopy groups, also referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed graphs at morphisms that induce isomorphisms on these groups…

For a contractive iterated function system (IFS), it is known that there is a natural hyperbolic graph structure (augmented tree) on the symbolic space of the IFS that reflects the relationship among neighboring cells, and its hyperbolic…

Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant…