A general form of Green Formula and Cauchy Integral Theorem
Julia Cufi, Joan Verdera
TL;DR
This paper extends Green's Formula and Cauchy's Integral Theorem to apply to any closed rectifiable curve in the plane, broadening their applicability beyond smooth curves.
Contribution
It introduces a generalized version of Green's Formula and Cauchy Integral Theorem valid for arbitrary closed rectifiable curves in the plane.
Findings
Green's Formula holds for all closed rectifiable curves
Cauchy Integral Theorem applies to arbitrary rectifiable curves
Broader applicability of classical complex analysis results
Abstract
We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.
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Taxonomy
Topicsadvanced mathematical theories · Mathematics and Applications · Algebraic Geometry and Number Theory