Jorge-Meeks $n$-noid plus 2 horizontal ends
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$n=3$, $r=0.4$.
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$n=4$, $r=5^{-1/4}$ (the most symmetric case).
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$n=7$, $r=0.9$.
Weierstrass Data
\[ M=\mathbb{C}\setminus(\{0\}\cup\{z\in\mathbb{C}\;;\;z^n=1\}),\] \[ g=\frac{z(r^nz^n-1)}{z^n-r^n},\qquad \eta = \frac{(z^n-r^n)^2}{z^2(z^n-1)^2}dz, \] where $n$ is an integer greater than 1, and $r\in (0,1)$ is a real constant.
The surface converges to Jorge-Meeks $n$-noid (resp. catenoid) as $r\to 0$ (resp. $r\to 1$).
