Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications

Details Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications

2008-04-23

arxiv.org/abs/0804.3761v2

Mathematics

Complex Variables

Scientific paper

We have obtained the explicit versions and precisions for the Hodge-Riemann decomposition of formes on affine algebraic curve V. The main application consists in the construction of Faddeev-Green function for Laplacian on V. Basing on this [HM](arXiv:0804.3951 and J.Geom.Anal., 2008,18), we extended from the case X in C to the case of bordered Riemann surface X in V the R.Novikov (1988) scheme for the effective reconstruction of conductivity function sigma on X through Dirichlet-to-Neumann mapping on bX for solutions of d(sigma d^cU)=0. In Sec.4 we give a correction of the paper [HM].

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