Abstract.
The following investigation deals with higher order variational integrals involving mean and Gaussian curvature of surfaces in Euclidean three-space. We prove that the few known examples of particular tori and cylinder surfaces are essentially the only possible solutions of the corresponding Euler equations in the classes of tubes and ruled surfaces.
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Received: 26.7.1996
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von der Mosel, H. Nonexistence results for extremals of curvature functionals. Arch. Math. 69, 427–434 (1997). https://doi.org/10.1007/s000130050141
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DOI: https://doi.org/10.1007/s000130050141