MINIMAL-SURFACES IN R(3) WITH DIHEDRAL SYMMETRY

We construct new examples of immersed minimal surfaces with catenoid e nds and finite total curvature, of both genus zero and higher genus. I n the genus zero case, we classify all such surfaces with at most 2n 1 ends, and with symmetry group the natural Z2 extension of the dihed ral group D(n). The surfaces are constructed by proving existence of t he conjugate surfaces. We extend this method to cases where the conjug ate surface of the fundamental piece is noncompact and is not a graph over a convex plane domain.