Complete minimal surfaces and minimal herissons (Q1110816)

The authors study a class W of minimal surfaces in \({\mathbb{R}}^ 3\) of finite total curvature C: up to a finite number of branch points the surfaces in W are complete. In other words, they are Abelian minimal surfaces in the sense of \textit{L. Bers} [J. Anal. Math. 1, 43-58 (1951; Zbl 0045.425)] with finite C. See also \textit{Y. W. Chen} [Ann. Math., II. Ser. 49, 790-806 (1948; Zbl 0038.331)]. In the present paper minimal herissons, surfaces in W with \(C=-4\pi\), are studied.