A contribution to the Calderón problem for Yang-Mills connections

Mihajlo Cekić

Published 2017-04-05Version 1

We consider the problem of identifying a unitary Yang-Mills connection $\nabla$ on a Hermitian vector bundle from the Dirichlet-to-Neumann (DN) map of the connection Laplacian $\nabla^*\nabla$ over compact Riemannian manifolds with boundary. We establish such uniqueness of the connection up to a gauge equivalence in the case of line bundles in the smooth category and for the higher rank case in the analytic category. Furthermore, we prove that on the restriction of the vector bundle to the boundary the DN map is an elliptic pseudodifferential operator of order one, whose full symbol determines the complete Taylor series of an arbitrary connection and a metric (also of an associated potential) at the boundary.