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arXiv · 1509.02645

Inverse problems for the connection Laplacian

Yaroslav Kurylev·Lauri Oksanen·Gabriel P. Paternain
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Abstract

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 Calderon problem for connections on a cylinder.

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Yaroslav Kurylev, Lauri Oksanen, Gabriel P. Paternain. 2015-09-09. Inverse problems for the connection Laplacian. https://arxiv.org/abs/1509.02645

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