Advertisement

Rendiconti del Circolo Matematico di Palermo

, Volume 11, Issue 1, pp 69–90 | Cite as

On the oriented Plateau Problem

  • Wendell H. Fleming
Article

Keywords

Minimal Surface Weak Sense Topological Type Simple Closed Curve Integral Current 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B] A. S. Besicovitch,Parametric surfaces III: Surfaces of minimum area, J. London Math. Soc.,23 (1948), 241–246; III, I. Nederl. Akad. Wetensch. Proc. Ser. A,57 (1954), 169–175.CrossRefMathSciNetGoogle Scholar
  2. [Cc] J. Cecconi,Sul teorema di Stokes, Rivista Mat. Univ. Parma,3 (1952), 233–264.zbMATHMathSciNetGoogle Scholar
  3. [Ce] L. Cesari,Surface Area, Princeton Univ. Press, 1956.Google Scholar
  4. [Co] R. Courant,Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience, 1950.Google Scholar
  5. [Fe 1] H. Federer,A note on the Gauss-Green theorem, Proc. Am. Math. Soc.,9 (1958), 447–451.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [Fe 2] H. Federer,Curvature measures, Trans. Am. Math. Soc.,93 (1959), 418–491.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Fe 3] H. Federer,The slicing of currents, to appear.Google Scholar
  8. [FF] H. Federer and W. H. Fleming,Normal and integral currents, Annals of Math.,72 (1960), 458–520.CrossRefMathSciNetGoogle Scholar
  9. [F] W. H. Fleming,An example in the problem of least area, Proc. Am. Math. Soc.,7 (1956), 1063–1074.CrossRefMathSciNetGoogle Scholar
  10. [FR] W. H. Fleming and R. Rishel,An integral formula for total gradient variation, Archiv der Math.,11 (1960), 218–222.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [G] E. de Giorgi,Nuovi teoremi relativi alle misure r—1 dimensionale in uno spazio ad r dimensioni, Ricerche Mat.,4 (1955), 95–113.MathSciNetGoogle Scholar
  12. [O] R. Osserman,Minimal surfaces in the large, Comm. Math. Helvetici,35 (1961), 65–76.zbMATHCrossRefMathSciNetGoogle Scholar
  13. [Ra] T. Radó,On the problem of Plateau, Ergebnisse d. Math. vol. 2, Springer, 1933.Google Scholar
  14. [Re 1] E. R. Reifenberg,Parametric surfaces V. Area II, Proc. London Math. Soc., Ser. 3,5 (1955), 342–357.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [Re 2] E. R. Reifenberg,Solution of the Plateau problem for m-dimensional surfaces of varying topological type, Acta Math.,104 (1960), 1–92.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [Rh] G. DeRham,Variétés Différentiables, Actualités Sci. Ind. vol. 1222, 1955.Google Scholar
  17. [Y1] L. C. Young,Surfaces paramétriques généralisées, Bull. Soc. Math. France,79 (1951), 59–84.zbMATHMathSciNetGoogle Scholar
  18. [Y2] L. C. Young,Contours on generalized and extremal varieties, J. Math. and Mech., 11 (1962), 615–646.zbMATHMathSciNetGoogle Scholar
  19. [Z] W. Ziemer,Integral currents mod. 2. Thesis, Brown University, 1961. To appear in Trans. Amer. Math. Soc.Google Scholar

Copyright information

© Springer 1962

Authors and Affiliations

  • Wendell H. Fleming
    • 1
  1. 1.ProvidenceU.S.A.

Personalised recommendations