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Transactions of the American Mathematical Society

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On certain minimum problems in the theory of convex curves


Author: Marlow Sholander
Journal: Trans. Amer. Math. Soc. 73 (1952), 139-173
MSC: Primary 52.0X
DOI: https://doi.org/10.1090/S0002-9947-1952-0053536-4
MathSciNet review: 0053536
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    T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, reprinted, New York, 1948. J. Favard, Problèmes d’extremums relatifs aux courbes convexes, I, II, Ann. École Norm. vol. 46 (1929) pp. 345-369; vol. 47 (1930) pp. 313-324. S. Fukasawa, Ein Maximum-problem der Eilinien, Tôhoku Math. J. vol. 26 (1926) pp. 27-34. T. Hayashi, The extremal chords of an oval, Tôhoku Math. J. vol. 22 (1923) pp. 387-393. S. Kawai, An inequality for the closed convex curve, Tôhoku Math. J. vol. 36 (1932) pp. 50-57. T. Kubota, Einige Ungleichheitsbeziehungen über Eilinien und Eiflächen, The Science Reports of the Tôhoku Imperial University Ser. 1 vol. 12 (1923) pp. 45-65. ---, Eine Ungleichheit für Eilinien, Math. Zeit. vol. 20 (1924) pp. 264-266. H. Lebesgue, Sur le problème des isopérimètres et sur les domaines de largeur constante, Bull. Soc. Math. France C. R. (1914) pp. 72-76. ---, Sur quelques questiones de minimum, relatives aux courbes orbiformes, et sur leur rapports avec le calcul des variations, J. Math. Pures Appl. (8) vol. 4 (1921) pp. 67-96. M. Yamanouti, Notes on closed convex figures, Proceedings of the Physico-Mathematical Society of Japan (3) vol. 14 (1932) pp. 605-609.

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Article copyright: © Copyright 1952 American Mathematical Society