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- W4301717967 abstract "We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-Delta_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that an admissible metric $g$ in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $Delta_g$. This is a constructive version of earlier uniqueness results by Dos Santos Ferreira et al. on admissible manifolds, and extends the reconstruction procedure of Nachman in Euclidean space. The main points are the derivation of a boundary integral equation characterizing the boundary values of complex geometrical optics solutions, and the development of associated layer potentials adapted to a cylindrical geometry." @default.
- W4301717967 created "2022-10-05" @default.
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- W4301717967 date "2010-11-02" @default.
- W4301717967 modified "2023-09-30" @default.
- W4301717967 title "Reconstructions from boundary measurements on admissible manifolds" @default.
- W4301717967 doi "https://doi.org/10.48550/arxiv.1011.0749" @default.
- W4301717967 hasPublicationYear "2010" @default.
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