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Transactions of the American Mathematical Society

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The isoperimetric inequality and the Lebesgue definition of surface area


Author: Tibor Radó
Journal: Trans. Amer. Math. Soc. 61 (1947), 530-555
MSC: Primary 27.2X
DOI: https://doi.org/10.1090/S0002-9947-1947-0021966-0
MathSciNet review: 0021966
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  • [1] P. Alexandroff and H. Hopf Topologie, Berlin, 1935.
  • [1] A. S. Besicovitch On the definition and the value of the area of a surface, Quart. J. Math. Oxford Ser. vol. 16 (1945) pp. 86-102. MR 0014415 (7:282a)
  • [1] W. Blaschke Kreis und Kugel, Leipzig, 1916.
  • [1] T. Bonnesen Les problèmes des isopérimètres et des isépiphanes, Paris, 1929.
  • [1] Z. Geöcze Sur l'exemple d'une surface dont l'aire est égale à zéro et gui remplit un cube, Bull. Soc. Math. France vol. 41 (1913) pp. 29-31.
  • [1] W. Gross Die Minimaleigenschaft der Kugel, Monatshefte für Mathematik und Physik vol. 18 (1917) pp. 77-97. MR 1548896
  • [1] H. D. Huskey Frécket polyhedra, Duke Math. J. vol. 11 (1944) pp. 417-425. MR 0011113 (6:121a)
  • [1] T. Radó Über das Flächenmass rektifizierbarer Flächen, Math. Ann. vol. 100 (1928) pp. 445-479. MR 1512495
  • [2] -On the problem of Plateau, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 2, 1933.
  • [3] -A lemma on the topological index, Fund. Math. vol. 27 (1936) pp. 212-225.
  • [4] -On continuous path-surfaces of zero area, Ann. of Math. vol. 44 (1943) pp. 173-191. MR 0007976 (4:224a)
  • [5] -On surface area, Proc. Nat. Acad. Sci. U. S. A. vol. 31 (1945) pp. 102-106. MR 0011712 (6:204f)
  • [1] S. Saks Theory of the integral, Warsaw, 1937.
  • [1] H. A. Schwarz Beweis des Satzes dass die Kugel kleinere Oberfläche besitzt als jeder andere Körper gleichen Volumens, Gesammelte Mathematische Abhandlungen, vol. 2, pp. 327-340.
  • [1] L. Tonelli Sulla propriétá minimo della sfera, Rend. Circ. Mat. Palermo vol. 39 (1915) pp. 1-30.
  • [1] J. W. T. Youngs Curves and surfaces, Amer. Math. Monthly vol. 51 (1944) pp. 1-11. MR 0009984 (5:233e)
  • [2] -The topological theory of Fréchet surfaces, Ann. of Math. vol. 45 (1944) pp. 753-785. MR 0012222 (6:278b)

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DOI: https://doi.org/10.1090/S0002-9947-1947-0021966-0
Article copyright: © Copyright 1947 American Mathematical Society

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