Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in Euclidean space
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We propose a new approach to solve the inverse boundary value problems in the Euclidean space. The idea consists of embedding the problem into hyperbolic manifolds and using their spectral properties. As a by-product, one can discuss the reconstruction of local conformal deformation of the metric of hyperbolic manifolds from the spectral data at infinity. We also propose a new spectral data observed from the cusp neighborhood at infinity.
- American journal of mathematics
American journal of mathematics 126(6), 1261-1313, 2004-12
The Johns Hopkins University Press