A general form of Green’s Formula and the Cauchy Integral Theorem

Cufí, Julià; Verdera, Joan

doi:10.1090/S0002-9939-2014-12418-X

A general form of Green’s Formula and the Cauchy Integral Theorem
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by Julià Cufí and Joan Verdera

Proc. Amer. Math. Soc. 143 (2015), 2091-2102

DOI: https://doi.org/10.1090/S0002-9939-2014-12418-X

Published electronically: December 4, 2014

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Abstract:

We prove a general form of Green’s Formula and the Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane. We use Vituśkin’s localization of singularities method and a decomposition of a rectifiable curve in terms of a sequence of Jordan rectifiable sub-curves due to Carmona and Cufí.

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