Related papers: Rigidity of diagonally embedded triangle groups

In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two consequences. The first is marked length pattern rigidity for arithmetic hyperbolic locally symmetric manifolds. The second is strengthen marked…

Let $G$ and $\tilde G$ be Kleinian groups whose limit sets $S$ and $\tilde S$, respectively, are homeomorphic to the standard Sierpi\'nski carpet, and such that every complementary component of each of $S$ and $\tilde S$ is a round disc. We…

Given a simplicial complex $K$, we consider several notions of geometric complexity of embeddings of $K$ in a Euclidean space ${\mathbb R}^d$: thickness, distortion, and refinement complexity (the minimal number of simplices needed for a PL…

In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict…

We prove that quasi-isometries of horospherical products of hyperbolic spaces are geometrically rigid in the sense that they are uniformly close to product maps, this is a generalisation of the result obtained by Eskin, Fisher and Whyte in…

Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a non-compact hyperbolic $3$-manifold such as a hyperbolic knot complement. We prove a rigidity result saying that if two non-elementary relatively…

In a discrete group generated by hyperplane reflections in the $n$-dimensional hyperbolic space, the reflection length of an element is the minimal number of hyperplane reflections in the group that suffices to factor the element. For a…

Hyperbolic inversive distance circle packings on the $2$-sphere correspond to Koebe polyhedra in the Beltrami-Klein model $\mathbb{B}^{3}$ of hyperbolic $3$-space. Koebe polyhedra are triangulated convex hyperbolic polyhedra with hyperideal…

We prove that level $5$ Witten-Reshetikhin-Turaev $\mathrm{SO}(3)$ quantum representations, also known as the Fibonacci representations, of mapping class groups are locally rigid. More generally, for any prime level $\ell$, we prove that…

If $\Gamma$ is the fundamental group of a complete finite volume hyperbolic $3$-manifold, Guilloux conjectured that the Borel function on the $\text{PSL}(n,\mathbb{C})$-character variety of $\Gamma$ should be rigid at infinity, that is it…

In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension $n\ge4$. Namely, we show that two convex isometric hypersurfaces are congruent locally around their corresponding under the…

In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a…

Let $F$ be a nonarchimedean local field of characteristic zero and let SL(N) = SL(N,F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the $K$-theory. We provide full arithmetic details. This…

We study the topological components of the surface group representations into $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{PSL}(2,\mathbb{R})$. Utilizing the signature formula established in [14], we determine the number of connected components…

There are 432 strongly squarefree symmetric bilinear forms of signature $(2,1)$ defined over $\Z[\sqrt{2}]$ whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. We classify all smooth…

We give a complete classification of complex hyperbolic $(n_1, n_2, n_3)$-triangle groups by types defined according to the ellipticity of two particular words of short length. This improves the Schwartz conjecture proved by Grossi.

We provide a lower bound for the embedding capacity of higher-dimensional symplectic ellipsoids, formulated in terms of the Lagrangian capacity of ellipsoids. Our approach relies on examining the Borman--Sheridan class of a Weinstein…

Many geometric structures associated to surface groups can be encoded in terms of invariant cross ratios on their circle at infinity; examples include points of Teichm\"uller space, Hitchin representations and geodesic currents. We add to…

This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its…