A COSTA-HOFFMAN-MEEKS TYPE SURFACE IN $\mathbb{H}^2 \times \mathbb{R}$

Abstract : We show the existence in the space $\mathbb{H}^2 \times \mathbb{R}$ of a family of embedded minimal surfaces of genus $1 \leq k < +\infty$ and finite total extrinsic curvature with two catenoidal type ends and one middle planar end. The proof is based on a gluing procedure.