Minimal surfaces in finite volume hyperbolic 3-manifolds N and in M × S1, M a finite area hyperbolic surface

We consider properly immersed finite topology minimal surfaces $\Sigma$ in complete finite volume hyperbolic$3$-manifolds $N$, and in $M\times{\Bbb S}^1$, where $M$ is a complete hyperbolic surface of finite area. We prove $\Sigma$ has finite total curvature equal to $2\pi$ times the Euler characteristic $\chi(\Sigma)$ of $\Sigma$, and we describe the geometry of the ends of $\Sigma$.