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November 2018 Inverse problems for the connection Laplacian
Yaroslav Kurylev, Lauri Oksanen, Gabriel P. Paternain
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J. Differential Geom. 110(3): 457-494 (November 2018). DOI: 10.4310/jdg/1542423627

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 Calderón problem for connections on a cylinder.

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Yaroslav Kurylev. Lauri Oksanen. Gabriel P. Paternain. "Inverse problems for the connection Laplacian." J. Differential Geom. 110 (3) 457 - 494, November 2018. https://doi.org/10.4310/jdg/1542423627

Information

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

zbMATH: 06982217
MathSciNet: MR3880231
Digital Object Identifier: 10.4310/jdg/1542423627

Rights: Copyright © 2018 Lehigh University

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Vol.110 • No. 3 • November 2018
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