NON-PROPERLY EMBEDDED MINIMAL PLANES IN HYPERBOLIC 3-SPACE

In this paper, we show that there are non-properly embedded minimal surfaces with finite topology in a simply connected Riemannian 3-manifold with non-positive curvature. We show this result by constructing a non-properly embedded minimal plane in H(3). Hence, this gives a counterexample to Calabi-Yau conjecture for embedded minimal surfaces in negative curvature case.