Journal of Differential Geometry

Inverse problems for the connection Laplacian

Yaroslav Kurylev, Lauri Oksanen, and 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 Calderón problem for connections on a cylinder.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1542423627

Digital Object Identifier
doi:10.4310/jdg/1542423627

Mathematical Reviews number (MathSciNet)
MR3880231

Zentralblatt MATH identifier
06982217

Citation

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. https://projecteuclid.org/euclid.jdg/1542423627


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