Decomposition of normal currents
HTML articles powered by AMS MathViewer
- by Maciej Zworski PDF
- Proc. Amer. Math. Soc. 102 (1988), 831-839 Request permission
Abstract:
As an answer to a question of Frank Morgan, it is shown that there exist normal currents which cannot be represented as convex integrals of rectifiable currents. However, under certain additional hypotheses, such decompositions exist. Examples are given to indicate that such hypotheses are necessary.References
-
J. B. Brothers (editor), Some open problems in geometric measure theory, Geometric Measure Theory and the Calculus of Variations (W. K. Allard and F. J. Almgren, eds.), Amer. Math. Soc., Providence, R. I., 1986.
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- Wendell H. Fleming and Raymond Rishel, An integral formula for total gradient variation, Arch. Math. (Basel) 11 (1960), 218–222. MR 114892, DOI 10.1007/BF01236935
- Robert M. Hardt and Jon T. Pitts, Solving Plateau’s problem for hypersurfaces without the compactness theorem for integral currents, Geometric measure theory and the calculus of variations (Arcata, Calif., 1984) Proc. Sympos. Pure Math., vol. 44, Amer. Math. Soc., Providence, RI, 1986, pp. 255–259. MR 840278, DOI 10.1090/pspum/044/840278 R. Harvey, Introduction to geometric measure theory, preprint.
- Frank Morgan, On finiteness of the number of stable minimal hypersurfaces with a fixed boundary, Indiana Univ. Math. J. 35 (1986), no. 4, 779–833. MR 865429, DOI 10.1512/iumj.1986.35.35042
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 831-839
- MSC: Primary 49F20; Secondary 53C35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934852-8
- MathSciNet review: 934852