Bulletin of the
Korean Mathematical Society BKMS

We construct three kinds of complete embedded singly-peri\-odic minimal surfaces in $\Bbb H^2\times \Bbb R$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\Bbb H^2\times \Bbb R$ by finite Scherk's towers.

Keywords: complete minimal surface, singly-periodic surface, product space

MSC numbers: Primary 53C42; Secondary 53A35, 53C40