The critical hyperbolic catenoid has Robin nullity 2 in mode |k|=1 and closed-form asymptotic radius r(a) = (3/2)log a + d_∞ + o(1) for large a and square-root degeneration near a=1/2.
Devyver,Index of the critical catenoid, Geom
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Robin nullity in mode $|k|=1$ and asymptotic radius of the critical hyperbolic catenoid
The critical hyperbolic catenoid has Robin nullity 2 in mode |k|=1 and closed-form asymptotic radius r(a) = (3/2)log a + d_∞ + o(1) for large a and square-root degeneration near a=1/2.