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| Abstract |
An anisotropic surface energy functional is the integral of an energy density function over a surface. The energy density depends on the surface normal at each point. The usual area functional is a sp...ecial case of such a functional. We study stationary surfaces of anisotropic surface energies in the euclidean three-space which are called anisotropic minimal surfaces. For any axisymmetric anisotropic surface energy, we show that, a surface is both a minimal surface and an anisotropic minimal surface if and only if it is a right helicoid. We also construct new examples of anisotropic minimal surfaces, which include zero mean curvature surfaces in the three-dimensional Lorentz-Minkowski space as special cases.show more
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2013A-9