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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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