Channel linear Weingarten surfaces. (English) Zbl 1348.53011

Summary: We demonstrate that every non-tubular channel linear Weingarten surface in Euclidean space is a surface of revolution, hence parallel to a catenoid or a rotational surface of non-zero constant Gauss curvature. We provide explicit parametrizations and deduce existence of complete hyperbolic linear Weingarten surfaces.


53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
Full Text: DOI arXiv Euclid