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Inverse Conductivity Problem on Riemann Surfaces

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Abstract

An electrical potential U on a bordered Riemann surface X with conductivity function σ>0 satisfies equation d(σ d c U)=0. The problem of effective reconstruction of σ from electrical currents measurements (Dirichlet-to-Neumann mapping) on the boundary: U| bX ↦ σ d c U| bX is studied. We extend to the case of Riemann surfaces the reconstruction scheme given, firstly, by R. Novikov (Funkc. Anal. Ego Priloz. 22:11–22, 2008) for simply connected X. We apply for this new kernels for \(\bar{ \partial }\) on the affine algebraic Riemann surfaces constructed in Henkin (arXiv:0804.3761, 2008).

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Authors and Affiliations

  1. Université Pierre et Marie Curie, Mathématiques, case 247, 4 place Jussieu, 75252, Paris, France

    Gennadi Henkin & Vincent Michel

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  1. Gennadi Henkin
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  2. Vincent Michel
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Correspondence to Gennadi Henkin.

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Communicated by Steven Krantz.

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Henkin, G., Michel, V. Inverse Conductivity Problem on Riemann Surfaces. J Geom Anal 18, 1033–1052 (2008). https://doi.org/10.1007/s12220-008-9035-x

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  • DOI: https://doi.org/10.1007/s12220-008-9035-x

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