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Proceedings of the American Mathematical Society

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A geometric inequality for plane curves with restricted curvature


Authors: G. D. Chakerian, H. H. Johnson and A. Vogt
Journal: Proc. Amer. Math. Soc. 57 (1976), 122-126
MSC: Primary 52A40
DOI: https://doi.org/10.1090/S0002-9939-1976-0402611-2
MathSciNet review: 0402611
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Abstract: A geometric proof is given that a closed plane curve of length $ L$ and curvature bounded by $ K$ can be contained inside a circle of radius $ L/4 - (\pi - 2)/2K$.


References [Enhancements On Off] (What's this?)

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  • [2] G. D. Chakerian and M. S. Klamkin, Minimal covers for closed curves, Math. Mag. 46 (1973), 55-61. MR 47 #2496. MR 0313944 (47:2496)
  • [3] L. E. Dubins, On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents, Amer. J. Math. 79 (1957), 497-516. MR 19, 678. MR 0089457 (19:678c)
  • [4] H. H. Johnson, An application of the maximum principle to the geometry of plane curves, Proc. Amer. Math. Soc. 44 (1974), 432-435. MR 50 #1128. MR 0348631 (50:1128)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0402611-2
Keywords: Plane curves, geometric inequalities, convexity
Article copyright: © Copyright 1976 American Mathematical Society

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