On conformal Lorentzian length spaces

Recently, Lorentzian length spaces have been introduced inspired by length spaces. One of the main objects of study in these spaces is a time separation function τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}, which is closely linked to their causal structure. In analogy to the metric d in length spaces, τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document} can express basic notions and many results in the setting of Lorentzian length spaces. In this paper, the concept of conformal Lorentzian length spaces is introduced and a novel version of limit curve theorem is proven. Finally, the global hyperbolic and causally simple Lorentzian length spaces are characterized.