Inverse problems for the connection Laplacian

By Yaroslav Kurylev, Lauri Oksanen, Gabriel P. Paternain. Journal of differential geometry, 2015

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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 Calderon problem for connections on a cylinder.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cdbfde662d8a7de12b50287322672ae3cf219503