W. Barrera

activity

20102026

most citedComparison theorems for Lorentzian length spaces with lower timelike curvature bounds

14 citations · 43 across the 18 of their papers we have counts for

collaborators

19 papers

math.CV2026

Unimodular Zeros of Selmer's Harmonic Trinomials

Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete

Let $n > k$ be positive integers and let $ε, δ \in {- 1, 1}$ . In this note, we classify the unimodular zeros of the harmonic trinomial $H_{\varepsilon,δ}:\mathbb{C}\to \mathbb…

math.DS2026

Asymptotic flag geometry of complex Kleinian groups in $P_{C}^{2}$

Waldemar Barrera, Angel Cano, Juan Pablo Navarrete +1

We organize several natural notions of limit set for discrete subgroups of $PSL (3, C)$ around a common asymptotic structure encoded by pseudo--projective degenerat…

math.CV2026

On the Parameter Spaces of Harmonic Trinomial Equations

Waldemar Barrera, Lucia Campa, Juan Pablo Navarrete

We analyze the parameter space of harmonic trinomial equations of the form $z^{n + m} + b z^{m} + c$ , where $n, m \in Z^{+}$ are coprime and $b, c \in C$ . Using version…

math.GR2023

Elementary groups in $\PSL(3,\C)$

Waldemar Barrera, Angel Cano, Juan Pablo Navarrete +1

In this paper, we give a classification of the subgroups of $PSL (3, C)$ that act on $P_{C}^{2}$ in such a way that their Kulkarni limit set has fi…

math.CA2023★ 1 cited

Egerváry's theorems for harmonic trinomials

Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete

In this manuscript, we study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficien…

math.DS2023

Action of $R$ -Fuchsian groups on $P_{C}^{n}$

W. Barrera, E. Montiel, J. P. Navarrete

We consider discrete subgroups of the group of orientation preserving isometries of the $m$ -dimensional hyperbolic space, whose limit set is a $(m - 1)$ -dimensional real sphere, acti…

math.CV2023★ 4 cited

The stability region for Schur stable trinomials with general complex coefficients

Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete

In this paper, we characterize the stability region for trinomials of the form $f (ζ) := a ζ^{n} + b ζ^{m} + c$ , $ζ \in C$ , where $a$ , $b$ and $c$ are non-zero complex numbers and $n…

math-ph2023

On the space of compact diamonds of Lorentzian length spaces

Waldemar Barrera, Luis Montes de Oca, Didier A. Solis

In this work we introduce the taxicab and uniform products for Lorentzian pre-length spaces. We further use these concepts to endow the space $D (R \times_{T} X)$ of causal diamonds wi…

math.DG2022★ 14 cited

Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds

Waldemar Barrera, Luis Montes de Oca, Didier A. Solis

In this article we introduce a notion of normalized angle for Lorentzian pre-length spaces. This concept allows us to prove some equivalences to the definition of timelike curvatur…

math.GT2022

Smooth Knot Limit Sets of the Complex Hyperbolic Plane

Waldemar Barrera, Rene Garcia, Juan Pablo Navarrete

It is shown that if a regular knot of class C2 is embedded in the boundary of the complex hyperbolic plane as the limit set of a discrete subgroup of PU(2, 1) then it is either a c…

math.CV2021★ 9 cited

On the number of roots for harmonic trinomials

Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete

In this manuscript we study the counting problem for harmonic trinomials of the form $a ζ^{n} + b ζ^{m} + c$ , where $n, m \in N$ , $n > m$ , and $a$ , $b$ and $c$ are non-zero com…

math.DS2021

A Family of Complex Kleinian Split Solvable Groups

Waldemar Barrera, Rene Garcia, Juan Pablo Navarrete

It is shown that lattices of a family of split solvable subgroups of PSL(N + 1, C) are complex Kleinian using techniques of Lie groups and dynamical systems, also that there exists…

math.MG2021★ 1 cited

On geodesic extendibility and the space of compact balls of length spaces

Waldemar Barrera, Luis M. Montes De Oca, Didier A. Solis

In this work we study the issue of geodesic extendibility on complete and locally compact metric length spaces. We focus on the geometric structure of the space $(Σ (X), d_{H})$ of com…

math.MG2019

On the metric geometry of the space of compact balls and the shooting property for length spaces

Waldemar Barrera, Luis Montes de Oca, Didier A. Solis

In this work we study the geodesic structure of the space $Σ (X)$ of compact balls of a complete and locally compact metric length space endowed with the Hausdorff distance $d_{H}$ . I…

math.DS2018★ 1 cited

Discrete parabolic groups in $PSL (3, C)$

Waldemar Barrera, Angel Cano, Juan Pablo Navarrete +1

We study and classify the purely parabolic discrete subgroups of $P S L (3, C)$ . This includes all discrete subgroups of the Heisenberg group $Heis (3, C)$ . While for $…

math.DS2010★ 9 cited

On the number of lines in the limit set for discrete subgroups of $P S L (3, C)$

Waldemar Barrera, A. Cano, Juan Pablo Navarrete

Given a discret subgroup $Γ\subset PSL(3,\C)$, we determine the number of complex lines and complex lines in general position lying in the complement of: maximal regions on which $…

math.DS2010★ 2 cited

A 2-dimensional Complex Kleinian Group With Infinite Lines in the Limit Set Lying in General Position

Waldemar Barrera, Angel Cano, Juan Pablo Navarrete

In this article we present an example of a discrete group $Σ_\C\subset PSL(3,\Bbb{R})$ whose action on $¶^{2}$ does no have invariant projective subspaces, is not conjugated to compl…

math.DG2010★ 2 cited

The limit set of discrete subgroups of $PSL(3,\C)$

Waldemar Barrera, Angel Cano, Juan Pablo Navarrete

If $Γ$ is a discrete subgroup of $P S L (3, C)$ , it is determined the equicontinuity region $E q (Γ)$ of the natural action of $Γ$ on $P_{C}^{2}$ . It is also proved that th…

math.DS2010

Subroups of $P S L (3, C)$ with four lines in general position in its Limit Set

Waldemar Barrera, Angel Cano, Juan Pablo Navarrete

In this article we provide an algebraic characterization of those groups of $P S L (3, C)$ whose limit set in the Kulkarni sense has, exactly, four lines in general position. Als…

Unimodular Zeros of Selmer's Harmonic Trinomials

Asymptotic flag geometry of complex Kleinian groups in PC2​

On the Parameter Spaces of Harmonic Trinomial Equations

Elementary groups in $\PSL(3,\C)$

Egerváry's theorems for harmonic trinomials

Action of R-Fuchsian groups on PCn​

The stability region for Schur stable trinomials with general complex coefficients

On the space of compact diamonds of Lorentzian length spaces

Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds

Smooth Knot Limit Sets of the Complex Hyperbolic Plane

On the number of roots for harmonic trinomials

A Family of Complex Kleinian Split Solvable Groups

On geodesic extendibility and the space of compact balls of length spaces

On the metric geometry of the space of compact balls and the shooting property for length spaces

Discrete parabolic groups in PSL(3,C)

On the number of lines in the limit set for discrete subgroups of PSL(3,C)

A 2-dimensional Complex Kleinian Group With Infinite Lines in the Limit Set Lying in General Position

The limit set of discrete subgroups of $PSL(3,\C)$

Subroups of PSL(3,C) with four lines in general position in its Limit Set

Asymptotic flag geometry of complex Kleinian groups in $P_{C}^{2}$

Action of $R$ -Fuchsian groups on $P_{C}^{n}$

Discrete parabolic groups in $PSL (3, C)$

On the number of lines in the limit set for discrete subgroups of $P S L (3, C)$

Subroups of $P S L (3, C)$ with four lines in general position in its Limit Set