The index of a plane curve and green's formula

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Abstract

In this paper we compute the line integral of a complex function on a rectifiable cycle homologous to zero obtaining a Green's formula with multiplicities that involves the ∂̄, of the function and the index of the cycle. We consider this formula in several settings and we obtain a sharp version in terms of the Lebesgue integrability properties of the partial derivatives of the function. This result depends on the proven fact that the index of a rectifiable cycle is square integrable with respect to the planar Lebesgue measure. © 2004 Springer.
Original languageEnglish
Pages (from-to)103-128
JournalRendiconti del Circolo Matematico di Palermo
Volume53
DOIs
Publication statusPublished - 1 Feb 2004

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