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