Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in Euclidean space

Abstract

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.