Scherk's Third Surface (Branched)
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Weierstrass Data
\[ M=(\mathbb{C}\cup\{\infty\})\setminus\{1,-1\}, \] \[ g=z,\qquad \eta = \frac{z}{(z^2-1)^3}dz. \] This surface is branched at $z=0$ and $z=\infty$.
Remark
In the paper
H. F. Scherk,
Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen,
J. Reine Angew. Math. 13 (1835), 185--208,
There are typos about this surface.
Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen,
J. Reine Angew. Math. 13 (1835), 185--208,
