Blatt, S., & Raffaelli, M. (2024). Existence of Optimal Flat Ribbons. Journal of Geometric Analysis, 34(8), 1–14. https://doi.org/10.1007/s12220-024-01683-w
Bending energy; Developable ribbon; Direct method in the calculus of variation; Gamma-convergence
en
Abstract:
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in R3 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.
