An estimate of the density at the boundary of an integral current modulo $v$
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- by Sandra O. Paur PDF
- Proc. Amer. Math. Soc. 62 (1977), 319-322 Request permission
Abstract:
An inequality is obtained which bounds the density at $z \in {{\mathbf {R}}^n}$ of the boundary of a $k + 1$ dimensional integral current modulo $\nu \;{(S)^\nu }$ by the density of ${(S)^\nu }$ at z. Also, the concept of boundary tangent developed in [3] is shown to be in agreement with Federer’s concept of a measuretheoretic exterior normal if $\nu = 0$ and S is obtained by integration over an ${\mathfrak {L}^n}$ measurable subset of ${{\mathbf {R}}^n}$.References
- John E. Brothers, Stokes’ theorem, Amer. J. Math. 92 (1970), 657–670. MR 274726, DOI 10.2307/2373367
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- Sandra O. Paur, Stokes’ theorem for integral currents modulo $\nu$, Amer. J. Math. 99 (1977), no. 2, 379–388. MR 482509, DOI 10.2307/2373825
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 319-322
- MSC: Primary 58A25; Secondary 49F20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0455005-9
- MathSciNet review: 0455005