Blatt S, Raffaelli M. Existence of Optimal Flat Ribbons.
JOURNAL OF GEOMETRIC ANALYSIS 2024;
34:250. [PMID:
38826622 PMCID:
PMC11139703 DOI:
10.1007/s12220-024-01683-w]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 04/24/2024] [Indexed: 06/04/2024]
Abstract
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in R 3 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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