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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Smooth interpolating curves of prescribed length and minimum curvature


Author: Joseph W. Jerome
Journal: Proc. Amer. Math. Soc. 51 (1975), 62-66
MSC: Primary 49A05; Secondary 41A05
MathSciNet review: 0380551
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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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0380551-4
PII: S 0002-9939(1975)0380551-4
Keywords: Minimum curvature, mean square curvature, interpolating, prescribed length, nonlinear open spline curve
Article copyright: © Copyright 1975 American Mathematical Society