Decomposition of normal currents

Author:
Maciej Zworski

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

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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.

**[B]**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.**[F]**H. Federer,*Geometric measure theory*, Springer-Verlag, Berlin and New York, 1969. MR**0257325 (41:1976)****[FR]**W. H. Fleming and R. Rishel,*An integral formula for total gradiant variation*, Arch. Math. II (1960), 218-222. MR**0114892 (22:5710)****[HP]**R. M. Hardt and J. T. Pitts,*Solving plateau problem for hypersurfaces without compactness theorem for integral currents*, Geometric Measure Theory and the Calculus of Variations, (W. K. Allard and F. J. Almgren, eds.), Amer. Math. Soc., Providence, R. I., 1986. MR**840278 (87j:49079)****[H]**R. Harvey,*Introduction to geometric measure theory*, preprint.**[M]**F. Morgan,*On finiteness of the number of stable minimal hypersurfaces with a fixed boundary*, Indiana Univ. Math. J.**35**(1986), 779-834. MR**865429 (88b:49059)**

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0934852-8

Article copyright:
© Copyright 1988
American Mathematical Society