Vol. 57, No. 2, 1975

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On Cauchy’s theorem for real algebraic curves with boundary

Norman Larrabee Alling

Vol. 57 (1975), No. 2, 315–321

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.

Mathematical Subject Classification 2000
Primary: 14H05
Secondary: 32G20, 30A52
Received: 16 November 1973
Published: 1 April 1975
Norman Larrabee Alling