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Existence of Optimal Flat Ribbons
Simon Blatt1, Matteo Raffaelli2
1Department of Mathematics, University of Salzburg, Hellbrunnerstraße 34, 5020 Salzburg, Austria.
Journal of Geometric Analysis
|June 3, 2024
Abstract:
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish.
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