Inverse Dirichlet-to-Neumann problem for nodal curves

This paper proposes direct and inverse results for the Dirichlet and Dirichlet-to-Neumann problems for complex curves with nodal type singularities. As an application, it gives a method for reconstructing the conformal structure of a compact surface of $\mathbb R^3$ with constant scalar conductivity from electric current density measurements in a neighbourhood of one of its points.
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