In this paper, we construct a one-parameter family of minimal surfaces in the
Euclidean 3-space of arbitrarily high genus and with three ends. Each member
of this family is immersed, complete and with finite total curvature. Another
interesting property is that the symmetry group of the genus k surfaces
Σk,x is the dihedral group with 4(k+1) elements. Moreover, in
particular, for ∣x∣=1 we find the family of the Costa-Hoffman-Meeks embedded
minimal surfaces, which have two catenoidal ends and a middle flat end.Comment: 17 figures, 17 page