Gel’fand–Calderón’s Inverse Problem for Anisotropic Conductivities on Bordered Surfaces in ℝ3

@article{Henkin2010GelfandCaldernsIP,
  title={Gel’fand–Calder{\'o}n’s Inverse Problem for Anisotropic Conductivities on Bordered Surfaces in ℝ3},
  author={Gennadi M. Henkin and Matteo Santacesaria},
  journal={International Mathematics Research Notices},
  year={2010},
  volume={2012},
  pages={781-809}
}
Let $X$ be a smooth bordered surface in $\real^3$ with smooth boundary and $\hat \sigma$ a smooth anisotropic conductivity on $X$. If the genus of $X$ is given, then starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on $\partial X$, we give an explicit procedure to find a unique Riemann surface $Y$ (up to a biholomorphism), an isotropic conductivity $\sigma$ on $Y$ and the boundary values of a quasiconformal diffeomorphism $F: X \to Y$ which transforms $\hat \sigma$ into… 

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