In this paper we study minimal surfaces in M × R, where M is a complete surface. Our main result is a Jenkins-Serrin type theorem which establishes necessary and sufficient conditions for the existence of certain minimal vertical graphs in M × R. We also prove that there exists a unique solution of the Plateau's problem in M × R whose boundary is a Nitsche graph and we construct a Scherk-type surface in this space.
We classify complete biharmonic surfaces with parallel mean curvature vector
field and non-negative Gaussian curvature in complex space forms.Comment: 15 page
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