Open AccessA general form of Green’s Formula and the Cauchy Integral Theorem
Author(s) -
Julià Cufí,
Jоan Verdera
Publication year - 2014
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-2014-12418-x
Subject(s) - mathematics , cauchy's integral formula , cauchy distribution , gravitational singularity , residue theorem , green's theorem , mathematical analysis , pure mathematics , methods of contour integration , cauchy's integral theorem , sequence (biology) , plane (geometry) , cauchy problem , geometry , initial value problem , picard–lindelöf theorem , danskin's theorem , fixed point theorem , chemistry , biochemistry
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.