On Calderon's problem for the connection Laplacian

We consider Calderón's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry of a vector bundle up to a gauge transformati...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2024-01, p.1-26
Main Authors: Gabdurakhmanov, Ravil, Kokarev, Gerasim
Format: Article
Language:English
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Summary:We consider Calderón's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry of a vector bundle up to a gauge transformation and an isometry of the base manifold.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2023.127