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Geometry and stability of surfaces with constant anisotropic mean curvature. (English) Zbl 1120.58010
The authors study the geometry of surfaces which are in equilibrium for a (constant coefficient) parametric elliptic functional with a volume constraint. They consider the first and second variations and exceptional set of the Gauss map for such surfaces. The equilibrium surfaces of revolution (anisotropic Delaunay surfaces) are also discussed, as the above functional is an anisotropic version of the Willmore functional.
MSC:
58E12Applications of variational methods to minimal surfaces