Elliptic special Weingarten surfaces of minimal type with finite total curvature satisfy an extended Jorge-Meeks formula; planes are the only ones with total curvature below 4π, and two-ended embedded surfaces are rotationally symmetric special catenoids.
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Elliptic special Weingarten surfaces of minimal type in $\mathbb{R}^3$ of finite total curvature
Elliptic special Weingarten surfaces of minimal type with finite total curvature satisfy an extended Jorge-Meeks formula; planes are the only ones with total curvature below 4π, and two-ended embedded surfaces are rotationally symmetric special catenoids.