Existence of a family of complete minimal surfaces of genus one with one end and finite total curvature (Q2752894)

The author reports on his recent result on the existence of a complex one-parameter family of complete minimal surfaces of genus one with one end and finite total curvature. Namely, he gives an outline of the proof for his result that there exists a complex one-parameter family of complete minimal surfaces of genus one with one end and total curvature less than \(-12 \pi\) and greater than \(-36 \pi\). One can obtain minimal surfaces from examples constructed by applying Weierstrass representation and the theory of elliptic functions. However, in the present paper, the author shows the existence of minimal surfaces in terms of Weierstrass representation without constructing examples by elliptic functions.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00049].