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Inverse Boundary Spectral Problems
© 2001 by Chapman & Hall/CRC. Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences. However, theExpand
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The Calderón problem in transversally anisotropic geometries
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier workExpand
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A graph discretization of the Laplace-Beltrami operator
We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operatorExpand
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Full-Wave Invisibility of Active Devices at All Frequencies
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 proveExpand
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Boundary regularity for the Ricci equation, geometric convergence, and Gel’fand’s inverse boundary problem
This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on theExpand
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Iterative time-reversal control for inverse problems
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptiveExpand
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Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded inExpand
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Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics
TLDR
We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves using a new class of artificially structured materials called metamaterials. Expand
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Isotropic transformation optics: approximate acoustic and quantum cloaking
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hiddenExpand
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Inverse problems for the connection Laplacian
We reconstruct a Riemannian manifold and a Hermitian vector bundle with compatible connection from the hyperbolic Dirichlet-to-Neumann operator associated with the wave equation of the connectionExpand
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