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Proceedings of the American Mathematical Society

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An estimate of the density at the boundary of an integral current modulo $ v$

Author: Sandra O. Paur
Journal: Proc. Amer. Math. Soc. 62 (1977), 319-322
MSC: Primary 58A25; Secondary 49F20
MathSciNet review: 0455005
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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}$.

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Keywords: Integral current modulo $ \nu$, density, tangent, measuretheoretic exterior normal
Article copyright: © Copyright 1977 American Mathematical Society

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