Some applications of the Dirichlet integral to the theory of surfaces
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- by L. C. Young
- Trans. Amer. Math. Soc. 64 (1948), 317-335
- DOI: https://doi.org/10.1090/S0002-9947-1948-0026118-7
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References
- A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions, Proc. Cambridge Philos. Soc. 41 (1945), 103–110. MR 12325, DOI 10.1017/s0305004100022453
- A. S. Besicovitch, On the definition and value of the area of a surface, Quart. J. Math. Oxford Ser. 16 (1945), 86–102. MR 14415, DOI 10.1093/qmath/os-16.1.86
- Lamberto Cesari, Criteri di uguale continuità ed applicazioni alla quadratura delle superficie, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2) 12 (1943), 61–84 (Italian). MR 17352 H. Lebesgue, Sur le problème de Dirichlet, Rend. Circ. Mat. Palermo vol. 24 (1907) pp. 371-402.
- E. J. McShane, Parametrizations of saddle surfaces, with application to the problem of plateau, Trans. Amer. Math. Soc. 35 (1933), no. 3, 716–733. MR 1501713, DOI 10.1090/S0002-9947-1933-1501713-3
- Charles B. Morrey Jr., An Analytic Characterization of Surfaces of Finite Lebesgue Area. Part I, Amer. J. Math. 57 (1935), no. 3, 692–702. MR 1507104, DOI 10.2307/2371197 T. Radó, On the problem of Plateau, Ergebnisse der Mathematik, vol. 2, Berlin, Springer, 1933. —, Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, New York, 1948. S. Saks, Theory of the integral, Monografje Mathematyczne, vol. 7, Warsaw, 1937.
- L. C. Young, A lemma in the theory of surfaces, J. London Math. Soc. 19 (1944), 209–212. MR 13778, DOI 10.1112/jlms/19.76_{P}art_{4}.209
- L. C. Young, On area and length, Fund. Math. 35 (1948), 275–302. MR 28934, DOI 10.4064/fm-35-1-275-302
Bibliographic Information
- © Copyright 1948 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 64 (1948), 317-335
- MSC: Primary 27.2X
- DOI: https://doi.org/10.1090/S0002-9947-1948-0026118-7
- MathSciNet review: 0026118