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On Calderon's problem for the connection Laplacian

Part of: Partial differential equations on manifolds; differential operators Elliptic equations and systems Miscellaneous topics - Partial differential equations Global differential geometry

Published online by Cambridge University Press:  05 January 2024

Ravil Gabdurakhmanov  and
Gerasim Kokarev
Ravil Gabdurakhmanov
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK (mmrg@leeds.ac.uk; g.kokarev@leeds.ac.uk)
Gerasim Kokarev
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK (mmrg@leeds.ac.uk; g.kokarev@leeds.ac.uk)
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Abstract

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.

Keywords

Calderón problemDirichlet-to-Neumann mapconnection Laplacian

MSC classification

Primary: 35R30: Inverse problems
Secondary: 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.) 35J47: Second-order elliptic systems 53C05: Connections, general theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 26
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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