## Costa-Hoffman-Meeks surface of genus $k$

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$k=3$, $c\approx 0.995117$.

### Weierstrass Data

$\overline{M}=\big\{(z,w)\in(\mathbb{C}\cup\{\infty\})^2\;;\;w^{k+1}=z^k(z^2-1)\big\},$ where $k$ is a positive integer. $M=\overline{M}\setminus\{(1,0),\,(-1,0),\,(\infty ,\infty)\},$ $g=\frac{c}{w},\qquad \eta = \frac{w}{z^2-1}dz,$ where $c$ is a positive real constant. For given $k$, we can choose $c$ so that $f$ is single valued on $M$.