An example of a minimal surface of genus one with two catenoid ends and one Enneper end

Abstract

In this paper we construct an example of a complete immersed minimal surface in $\mathbb{R}^3$ of genus one with two embedded catenoid-type ends, one Enneper-type end and total Gauss curvature $-16\pi.$ The proof of the existence of this example, was obtained using the Weierstrass representation, the theory of elliptic functions and explicitly solving the period problem.