Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{H}^1}$$\end{document} with low regularity

We give new examples of entire area-minimizing t-graphs in the sub-Riemannian Heisenberg group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{H}^1}$$\end{document}. They are locally Lipschitz in Euclidean sense. Some regular examples have prescribed singular set consisting of either a horizontal line or a finite number of horizontal halflines extending from a given point. Amongst them, a large family of area-minimizing cones is obtained.