On the stable recovery of a metric from the hyperbolic DN map with incomplete data | Zendy

Plamen Stefanov | Zendy; Günther Uhlmann | Zendy; András Vasy | Zendy

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On the stable recovery of a metric from the hyperbolic DN map with incomplete data

Author(s) -

Plamen Stefanov,

Günther Uhlmann,

András Vasy

Publication year - 2016

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2016035

Subject(s) - uniqueness , riemannian manifold , mathematics , boundary (topology) , dirichlet distribution , metric (unit) , hyperbolic 3 manifold , mathematical analysis , manifold (fluid mechanics) , statistical manifold , neumann boundary condition , hyperbolic tree , conformal map , hyperbolic group , hyperbolic manifold , pure mathematics , information geometry , boundary value problem , hyperbolic function , geometry , curvature , scalar curvature , mechanical engineering , operations management , engineering , economics

We show that given two hyperbolic Dirichlet to Neumann maps associated to two Riemannian metrics of a Riemannian manifold with boundary which coincide near the boundary are close then the lens data of the two metrics is the same. As a consequence, we prove uniqueness of recovery a conformal factor (sound speed) locally under some conditions on the latter.

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