We prove the existence of a compact genus one immersed minimal surface M, whose boundary is the union of two immersed locally convex curves lying in parallel planes. M is a part of a complete minimal surface with two finite total curvature ends.
Cite this article
Barbara Nelli, An example of an immersed complete genus one minimal surface in with two convex ends. Comment. Math. Helv. 73 (1998), no. 2, pp. 298–305DOI 10.1007/S000140050056