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Higher-order elastics and elastic hulls. (English) Zbl 1283.49061
Summary: By higher-order elastics we mean solutions of the problem to minimize integrals of quadratic forms of curvatures of multidimensional curves. Differential equations of second-order elastics (minimizing a quadratic form of the curvature and torsion of the curve) are obtained. Surfaces minimizing integrals of the squared Gaussian curvature are found.

MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
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