SINGLY-PERIODIC MINIMAL SURFACES IN ℍ2×ℝ

We construct three kinds of complete embedded singly-peri-odic minimal surfaces in H 2 R. The rst one is a 1-parameter family ofminimal surfaces which is asymptotic to a horizontal plane and a verticalplane; the second one is a 2-parameter family of minimal surfaces whichhas a fundamental piece of nite total curvature and is asymptotic to a nite number of vertical planes; the last one is a 2-parameter family ofminimal surfaces which ll H 2 R by nite Scherk’s towers. 1. IntroductionIn this paper we construct complete embedded singly-periodic minimal sur-faces in H 2 R. The study of minimal surfaces in H 2 R was initiated by Nelliand Rosenberg [10, 12]. By several mathematicians, some interesting examplesare found as follows: the catenoid that is a surface of revolution about thevertical R-axis; the helicoid that is ruled by the horizontal geodesic; the Rie-mann type minimal surface that is foliated by horizontal circles and geodesics;the Jenkins-Serrin type minimal surface that is a minimal graph over a do-main bounded by an ideal polygon and is asymptotic to vertical planes; the