A planar end between two catenoid ends (finite Riemann 1)
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$\rho =0.1$
Weierstrass Data
\[ M=\mathbb{C}\setminus\{1,-1\},\qquad g=\rho\frac{z^2+3}{z^2-1},\qquad \eta = dz, \] where $\rho\gt 0$ is a constant called the López-Ros parameter.