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A Parametric Gauss-Green Theorem in Several Variables

Published online by Cambridge University Press:  20 November 2018

M. Ortel  and
W. Schneider
M. Ortel
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii, 96822
W. Schneider
Affiliation:
Department of Mathematics, Carleton University, Ottawa, Ontario K1S 5B6
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Abstract

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We present a short, computational proof of the parametric Gauss-Green theorem for a broad class of closed chains. The proof involves only measure theory and the basic theory of differential forms: in particular, no constructions from topology are used. For completeness, the standard properties of winding numbers are also established by methods from analysis.

Keywords

26B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 156 - 165
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. [FED 1] Fédérer, H., Geometric measure theory, Springer, New York, 1969.Google Scholar
2. [FED 2] Fédérer, H., Slices and potentials, Indiana Univ. Math. J., Vol. 21, No. 4 (1971).Google Scholar
3. [M 1] Michael, J. H., An approximation to a rectifiable plane curve, J. London Math Soc. 30 (1955), 1-11.Google Scholar
4. [M 2] Michael, J. H., Integration over parametric surfaces, Proc. London Math. Soc. 7 (1957), 616-640.Google Scholar
5. [OS 1] Ortel, M. and Schneider, W., The parametric Gausss-Green theorem, Proc. Am. Math. Soc. 98 (1986), 615-618.Google Scholar