Smooth interpolating curves of prescribed length and minimum curvature
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- by Joseph W. Jerome PDF
- Proc. Amer. Math. Soc. 51 (1975), 62-66 Request permission
Abstract:
It is shown that, among all smooth curves of length not exceeding a prescribed upper bound which interpolate a finite set of planar points, there is at least one which minimizes the curvature in the ${L^2}$ sense. Thus, we show to be sufficient for the solution of the problem of minimum curvature a condition, viz., prescribed length, which has been known to be necessary for at least a decade. The proof extends immediately to curves in ${{\mathbf {R}}^n},n > 2$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 62-66
- MSC: Primary 49A05; Secondary 41A05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0380551-4
- MathSciNet review: 0380551