INVERSE PROBLEMS FOR THE CONNECTION LAPLACIAN
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Kurylev, Yaroslav
Oksanen, Lauri
Paternain, Gabriel P
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 Calderon problem for connections on a cylinder.
Description
Keywords
math.AP, math.AP, math.DG, 35R30
Journal Title
JOURNAL OF DIFFERENTIAL GEOMETRY
Conference Name
Journal ISSN
0022-040X
1945-743X
1945-743X
Volume Title
110
Publisher
International Press of Boston
Publisher DOI
Sponsorship
YK was partially supported by the EPSRC grant EP/L01937X/1 and CNRS, LO by the EPSRC grant EP/L026473/1 and Fondation Sciences Mathématiques de Paris, and GPP by the EPSRC grant EP/M023842/1 and CNRS.