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Geometry of the anisotropic minimal surfaces. (English) Zbl 1289.53012
Summary: A simple modification of the surface tension in the axisymmetric case leads to analogues of the Delaunay surfaces. Here, we derive an explicit parameterization of the most simple case of this new class of surfaces which can be considered as a generalization of the catenoids. The geometry of these surfaces depends on two real parameters and are studied in some detail.
MSC:
53A05 Surfaces in Euclidean and related spaces
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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