# New complete embedded minimal surfaces in H2xR - Mathematics > Differential Geometry

Abstract: We construct three kinds of complete embedded minimal surfaces in $\BbbH^2\times \Bbb R$. The first is a simply connected, singly periodic, infinitetotal curvature surface. The second is an annular finite total curvaturesurface. These two are conjugate surfaces just as the helicoid and the catenoidare in $\mathbb R^3$. The third one is a finite total curvature surface whichis conformal to $\mathbb S^2\setminus\{p 1, .,p k\}, k\geq3.$

Author: Juncheol Pyo

Source: https://arxiv.org/