On Cauchy’s theorem for real algebraic curves with boundary
Norman L. Alling · Pacific Journal of Mathematics · 1975
On a real algebraic curve with a nonempty boundary, one must orient the several boundary components in order to pose the question considered in Cauchy's theorem for analytic differentials.It is proved that the conclusion of Cauchy's theorem is true, in this context, if and only if the orientation in question is induced by an orientation of the interior of the curve.