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A Version of the Stokes Theorem Using Test Curves
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Journal Article
A Version of the Stokes Theorem Using Test Curves
2020
Overview
We prove that a parametric Lipschitz surface of codimension 1 in a smooth manifold induces a boundary in the sense of currents (roughly speaking, surrounds a “domain” with an eventual multiplicity and together with it forms a pair for the Stokes theorem) if and only if it passes a test in terms of crossing the surface by “almost all” curves. We use the AM-modulus recently introduced in [22] to measure the exceptional family of curves.
Publisher
Indiana University Mathematics Department
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