Catenoid is a minimal surface
= Catenoid is a minimal surface
For the standard catenoid, the two <principal curvature>[principal curvatures] are opposite, so its <mean curvature> vanishes. Its <Gaussian curvature> is $K=-\operatorname{sech}^4u<0$, which also shows that no neighbourhood is <local isometry>[locally isometric] to a plane, cylinder, or regular part of a cone, all of which have zero Gaussian curvature.