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An electrical potential U on bordered surface X (in Euclidienthree-dimensional space) with isotropic conductivity function sigma>0 satisfiesequation d(sigma d^cU)=0, where d^c is real operator associated with complex(conforme) structure on X induced by Euclidien metric of three-dimensionalspace. This paper gives exact reconstruction of conductivity function sigma onX from Dirichlet-to-Neumann mapping (for aforementioned conductivity equation)on the boundary of X. This paper extends to the case of the Riemann surfacesthe reconstruction schemes of R.Novikov (1988) and of A.Bukhgeim (2008) givenfor the case of domains in two-dimensional Euclidien space. The paper extendsand corrects the statements of Henkin-Michel (2008), where the inverse boundaryvalue problem on the Riemann surfaces was firstly considered.

On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary