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

Gennadi Henkin (1)

1 IMJ - Institut de Mathématiques de Jussieu

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].

Mots clés: Riemann surface; Inverse conductivity problem; dbar method; Homotopy formulas

Domaines: Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]

Gennadi Henkin. Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications. 2010. ⟨hal-00275361v2⟩