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


Authors: Julià Cufí and Joan Verdera
Journal: Proc. Amer. Math. Soc. 143 (2015), 2091-2102
MSC (2010): Primary 26B20, 30C99; Secondary 31A10
DOI: https://doi.org/10.1090/S0002-9939-2014-12418-X
Published electronically: December 4, 2014
MathSciNet review: 3314118
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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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Additional Information

Julià Cufí
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia
Email: jcufi@mat.uab.cat

Joan Verdera
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia
Email: jvm@mat.uab.cat

DOI: https://doi.org/10.1090/S0002-9939-2014-12418-X
Received by editor(s): June 28, 2013
Received by editor(s) in revised form: October 21, 2013
Published electronically: December 4, 2014
Additional Notes: This work was partially supported by the grants 2009SGR420 (Generalitat de Catalunya) and MTM2010-15657 (Ministerio de Educación y Ciencia)
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society

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