Commentarii Mathematici Helvetici


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Volume 73, Issue 2, 1998, pp. 298–305
DOI: 10.1007/s000140050056

Published online: 1998-06-30

An example of an immersed complete genus one minimal surface in $ \Bbb {R}^3 $ with two convex ends

B. Nelli[1]

(1) Università di Pisa, Italy

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.

Keywords: Minimal surface, convex boundary, Weierstrass representation, elliptic functions

Nelli B.: An example of an immersed complete genus one minimal surface in $ \Bbb {R}^3 $ with two convex ends. Comment. Math. Helv. 73 (1998), 298-305. doi: 10.1007/s000140050056