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

Hiroshi Isozaki | Zendy

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

Author(s) -

Hiroshi Isozaki

Publication year - 2004

Publication title -

american journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.818

H-Index - 67

eISSN - 1080-6377

pISSN - 0002-9327

DOI - 10.1353/ajm.2004.0047

Subject(s) - mathematics , hyperbolic space , conformal map , embedding , euclidean geometry , inverse , hyperbolic manifold , cusp (singularity) , euclidean space , infinity , mathematical analysis , manifold (fluid mechanics) , boundary (topology) , metric (unit) , inverse problem , space (punctuation) , pure mathematics , hyperbolic function , geometry , computer science , mechanical engineering , operations management , artificial intelligence , engineering , economics , operating system

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

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