arXiv subjects

Luis Montes de Oca

Publications and source records attributed to Luis Montes de Oca.

3 recordsLinked to original sources

arXiv2023

On the space of compact diamonds of Lorentzian length spaces

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 with a Lorentzian length space structure, closely relating its causal properties with its geometry as a metric space furnished with its associated Hausdorff distance. Among the general results, we show that this space is geodesic and globally hyperbolic for complete $X$.

math-ph↗

arXiv2022

Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds

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 curvature bounds from below for Lorentzian pre-length spaces. Specifically, we establish some comparison theorems known as the local Lorentzian version of the Toponogov theorem and the Alexandrov convexity property. Finally, as an application we obtain a first variation Formula for non-negatively curved globally hyperbolic Lorentzian length spaces.

math.DG↗

arXiv2019

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

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 $d_H$. In particular, we focus on a geometric condition (referred to as the shooting property) that enables us to give an explicit isometry between $(Σ(X),d_H)$ and the closed half-space $ X\times \mathbb{R}_{\ge 0}$ endowed with a taxicab metric.

math.MG↗