We construct embedded minimal surfaces of finite total curvature in euclidean space by gluing catenoids and planes. We use Weierstrass Representation and we solve the Period Problem using the Implicit Function Theorem. As a corollary, we obtain the existence of minimal surfaces with no symmetries.
"An Embedded Minimal Surface with no Symmetries." J. Differential Geom. 60 (1) 103 - 153, January, 2002. https://doi.org/10.4310/jdg/1090351085