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

2008/04/23 by Gennadi M. Henkin, Gennadi Henkin, Henkin, Gennadi · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Mathematical and Theoretical Analysis #advanced mathematical theories #math.AP #math.CV #msc:32S65 #msc:32V20 #msc:35R30 #msc:58J32

paper · pdf · doi:10.48550/arxiv.0804.3761

arxiv created 2010/01/10 · arxiv updated 2010/01/13

Abstract

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].

Citations

• Inverse conductivity problem on Riemann surfaces

Cited by

• Inverse conductivity problem on Riemann surfaces

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