Morrey's representation theorem for surfaces in metric spaces.
E. Silverman
Source: Pacific J. Math. Volume 7, Number 4 (1957), 1677-1690.
Primary Subjects: 28.0X
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pjm/1103043239
Zentralblatt MATH identifier:
0079.27901
Mathematical Reviews number (MathSciNet):
MR0092849
References
[1] S. Banach, Theorie des operations lneaires, Warsaw, 1932.
[2] L. Cesari, Criteri di uguale continuita ed applicazon alia quadratura delle super- ficie, Ann. Scuola Norm. Sup. Pisa, (2) 12 (1943), 61-84.
Mathematical Reviews (MathSciNet):
MR8:142e
Zentralblatt MATH:
0061.11002
[3] L. Cesari, An existence theorem of variations for integrals on parametricsurfaces, Amer. J. Math., 74 (1952), 265-295.
Mathematical Reviews (MathSciNet):
MR14:292b
Zentralblatt MATH:
0046.10901
[4] L. Cesari, Surface area, Ann. of Math. Studies 35, Princeton, 1956.
Mathematical Reviews (MathSciNet):
MR17:596b
Zentralblatt MATH:
0073.04101
[5] J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc, 40 (1936),396-414.
Mathematical Reviews (MathSciNet):
MR1501880
Zentralblatt MATH:
0015.35604
[6] J. M. Danskin, On the existence of minimizing surfaces in parametric double integral problems of the calculus of variations, Riv. Mat. Univ. Parma, 3 (1952), 43-63.
Mathematical Reviews (MathSciNet):
MR14:292a
Zentralblatt MATH:
0048.08104
[7] E. J. McShane, Integration, Princeton, 1947.
[8] C. B. Morrey, A class of representationsof manifolds,Amer. J. Math., 55 (1933), 683-707.
[9] C. B. Morrey, An analytic characterizationof surfaces of finite Lebesgue area, Amer. J. Math., 57 (1935),
[10] C. B. Morrey, Multiple integral problems in the calculus of variations and related topics, Univ. of California, (N.S.) 1 (1943), 1-130.
Mathematical Reviews (MathSciNet):
MR6:180b
Zentralblatt MATH:
0108.10402
[11] C. B. Morrey, The problem of Plateau on a Riemannian manifold, Ann. of Math., (2) 49 (1948), 807-851.
Mathematical Reviews (MathSciNet):
MR10:259f
Zentralblatt MATH:
0033.39601
[12] A. G. Sigalov, Two-dimensional problems of the calculus of variations, Uspehi Mat. Nauk. (N.S.) 6. no. 2, 42 (1951), 16-101, Amer. Math. Soc. Translation Number 83.
Mathematical Reviews (MathSciNet):
MR13:257d
[13] E. Silverman, Definitions of Lebesque area for surfaces in metric spaces, Riv. Mat. Univ. Parma, 2 (1951), 47-76.
Mathematical Reviews (MathSciNet):
MR13:122a
Zentralblatt MATH:
0043.05702
Pacific Journal of Mathematics
