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In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet(More)
Revised Abstract There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or " cloaking ") from observation by electromagnetic (EM) waves. Here, we prove invisibility with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. The basic idea, as(More)
We prove that a potential q can be reconstructed from the Dirichlet-to-Neumann map for the Schrödinger operator −∆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 ∆g. This is a constructive version of earlier(More)