Sami Douba

activity

20192026

most citedCubulated hyperbolic groups admit Anosov representations

3 citations · 4 across the 21 of their papers we have counts for

collaborators

26 papers

math.GT2026

On local minimality of Hausdorff dimension for round limit sets

Sami Douba, Andrés Sambarino, Franco Vargas Pallete

We address a question of Canary--Taylor and Canary--Minsky--Taylor for sufficiently symmetric compact hyperbolic $3$ -orbifolds with totally geodesic boundary. We give sufficient co…

math.GT2026

Complex hyperbolic surfaces whose closed geodesics are all simple

Sami Douba, D. B. McReynolds, Julien Paupert +1

We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Pra…

math.GT2026

On topologically transitive subsets of flag manifolds

Subhadip Dey, Sami Douba, Konstantinos Tsouvalas

We discuss some contexts in which the topological dynamics of certain Anosov subgroups of higher-rank Lie groups on "bad" subsets of flag manifolds can be analyzed using results fr…

math.GT2026

Convex cocompact right-angled Gromov-Thurston polyhedra

Sami Douba

Lee and Marquis exhibited convex cocompact hyperbolic reflection groups in dimension 5 whose limit sets are homeomorphic to the 3-sphere, but none of whose finite-index subgroups c…

math.GR2026

On transversality in flag manifolds and linearity of amalgams

Sami Douba, Konstantinos Tsouvalas

We show that the fundamental group of the double of a complete negatively curved locally symmetric manifold along a closed geodesic is linear. More generally, we establish linearit…

math.GT2026

Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio

Sami Douba, Franco Vargas Pallete

We exhibit, for any $n \geq 3$ , infinitely many pairwise incommensurable complete finite-volume hyperbolic $n$ -manifolds, both compact and noncompact, each with nonempty totally ge…

math.GR2026

Convex cocompact groups with three-dimensional limit sets

Sami Douba, Gye-Seon Lee, Ludovic Marquis +1

We provide a general construction of convex cocompact hyperbolic reflection groups with three-dimensional limit sets. More precisely, our construction takes as input an arbitrary s…

math.GR2026

Quasihomomorphisms to real algebraic groups

Sami Douba, Francesco Fournier-Facio, Sam Hughes +1

A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in di…

math.GR2026

Matrix entries, unipotents, and linearity of amalgams

Sami Douba, Konstantinos Tsouvalas

We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of l…

math.GT2025

On reflections of congruence hyperbolic manifolds

Sami Douba, Franco Vargas Pallete

We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed poi…

math.GR2025

Ping-pong in the projective plane over a nonarchimedean field

Sami Douba, Dmitry Kubrak, Konstantinos Tsouvalas

We show that any lattice in $SL_{3} (k)$ , where $k$ is a nonarchimedean local field, contains an undistorted subgroup isomorphic to the free product $Z^{2} * Z$ …

math.GT2025

Zariski-Closures of Linear Reflection Groups

Jacques Audibert, Sami Douba, Gye-Seon Lee +1

We give necessary and sufficient conditions for a linear reflection group in the sense of Vinberg to be Zariski-dense in the ambient projective general linear group. As an applicat…

math.GT2025

Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere

Sami Douba, Gye-Seon Lee, Ludovic Marquis +1

We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by $50$ reflections of $\ma…

math.GT2024

Density of systoles of hyperbolic manifolds

Sami Douba, Junzhi Huang

We show that for each $n \geq 2$ , the systoles of closed hyperbolic $n$ -manifolds form a dense subset of $(0, + \infty)$ . We also show that for any $n \geq 2$ and any Salem number $λ…

math.GR2023★ 1 cited

Systoles of hyperbolic hybrids

Sami Douba

We exhibit closed hyperbolic manifolds with arbitrarily small systole in each dimension that are not quasi-arithmetic in the sense of Vinberg, and are thus not commensurable to tho…

math.GR2023★ 3 cited

Cubulated hyperbolic groups admit Anosov representations

Sami Douba, Balthazar Fléchelles, Theodore Weisman +1

We prove that any hyperbolic group acting properly discontinuously and cocompactly on a $CAT (0)$ cube complex admits a projective Anosov representation into $\mathrm{SL}(d…

math.GR2023

Infinitely many commensurability classes of compact Coxeter polyhedra in $H^{4}$ and $H^{5}$

Nikolay Bogachev, Sami Douba, Jean Raimbault

We prove that certain families of compact Coxeter polyhedra in 4- and 5-dimensional hyperbolic space constructed by Makarov give rise to infinitely many commensurability classes of…

math.GR2023

On regular subgroups of $SL_{3} (R)$

Sami Douba, Konstantinos Tsouvalas

Motivated by a question of M. Kapovich, we show that the $Z^{2}$ subgroups of $SL_{3} (R)$ that are regular in the language of Kapovich--Leeb--Porti, or diver…

math.GR2023

A novel witness to incoherence of $SL_{5} (Z)$

Sami Douba

Motivated by a question of Stover, we discuss an example of a Zariski-dense finitely generated subgroup of $SL_{5} (Z)$ that is not finitely presented.

math.GT2023

Geometric and arithmetic properties of Löbell polyhedra

Nikolay Bogachev, Sami Douba

The Löbell polyhedra form an infinite family of compact right-angled hyperbolic polyhedra in dimension $3$ . We observe, through both elementary and more conceptual means, that the…

math.GR2022

Anosov groups that are indiscrete in rank one

Sami Douba, Konstantinos Tsouvalas

We exhibit Anosov subgroups of $SL_{d} (R)$ that do not embed discretely in any rank- $1$ simple Lie group of noncompact type, or indeed, in any finite product of suc…

math.GR2022

A hyperbolic lattice in each dimension with Zariski-dense surface subgroups

Sami Douba

For each integer $n \geq 3$ , we exhibit a nonuniform arithmetic lattice in $SO (n, 1)$ containing Zariski-dense surface subgroups.

math.GR2021

Thin right-angled Coxeter groups in some uniform arithmetic lattices

Sami Douba

Using a variant of an unpublished argument due to Agol, we show that an irreducible right-angled Coxeter group on $n \geq 3$ vertices embeds as a thin subgroup of a uniform arith…

math.GR2021

Proper CAT(0) actions of unipotent-free linear groups

Sami Douba

Let $Γ$ be a finitely generated group of matrices over $C$ . We construct an isometric action of $Γ$ on a complete CAT(0) space $X$ such that the restriction of this action…

On local minimality of Hausdorff dimension for round limit sets

Complex hyperbolic surfaces whose closed geodesics are all simple

On topologically transitive subsets of flag manifolds

Convex cocompact right-angled Gromov-Thurston polyhedra

On transversality in flag manifolds and linearity of amalgams

Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio

Convex cocompact groups with three-dimensional limit sets

Quasihomomorphisms to real algebraic groups

Matrix entries, unipotents, and linearity of amalgams

On reflections of congruence hyperbolic manifolds

Ping-pong in the projective plane over a nonarchimedean field

Zariski-Closures of Linear Reflection Groups

Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere

Density of systoles of hyperbolic manifolds

Systoles of hyperbolic hybrids

Cubulated hyperbolic groups admit Anosov representations

Infinitely many commensurability classes of compact Coxeter polyhedra in H4 and H5

On regular subgroups of SL3​(R)

A novel witness to incoherence of SL5​(Z)

Geometric and arithmetic properties of Löbell polyhedra

Anosov groups that are indiscrete in rank one

A hyperbolic lattice in each dimension with Zariski-dense surface subgroups

Thin right-angled Coxeter groups in some uniform arithmetic lattices

Proper CAT(0) actions of unipotent-free linear groups

Infinitely many commensurability classes of compact Coxeter polyhedra in $H^{4}$ and $H^{5}$

On regular subgroups of $SL_{3} (R)$

A novel witness to incoherence of $SL_{5} (Z)$