Abstract Consider the energy E α Σ = ∫ Σ | p | α d Σ E_=_ p^\, d, where Σ is a surface in Euclidean space R 3 R^3 and α ∈ R. We prove that planes and spheres are the only stationary surfaces for E α E_ with constant Gauss curvature. We also characterize these surfaces assuming that a principal curvature is constant or that the mean curvature is constant.
Rafael López (Wed,) studied this question.
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