Generalizations of the Cauchy Integral Theorems

Details Generalizations of the Cauchy Integral Theorems Generalizations of the Cauchy Integral Theorems

2011-01-02

arxiv.org/abs/1101.0385v2

Mathematics

Complex Variables

10 pages, 3 figures

Scientific paper

We extend the Cauchy residue theorem to a large class of domains including differential chains that represent, via canonical embedding into a space of currents, divergence free vector fields and non-Lipschitz curves. That is, while the classical Cauchy theorems involve integrals over piecewise smooth parameterized curves, these classical theorems actually hold for far more general notions of "curve." We also extend the definition of winding number to these domains and show that it behaves as expected.

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