Journal of Differential Geometry

Inverse problems for the connection Laplacian

Yaroslav Kurylev, Lauri Oksanen, and Gabriel P. Paternain

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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 connection Laplacian. The boundary data is local and the reconstruction is up to the natural gauge transformations of the problem. As a corollary we derive an elliptic analogue of the main result which solves a Calderón problem for connections on a cylinder.

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J. Differential Geom., Volume 110, Number 3 (2018), 457-494.

Received: 14 September 2015
First available in Project Euclid: 17 November 2018

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Kurylev, Yaroslav; Oksanen, Lauri; Paternain, Gabriel P. Inverse problems for the connection Laplacian. J. Differential Geom. 110 (2018), no. 3, 457--494. doi:10.4310/jdg/1542423627.

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