Inverse problems for the connection Laplacian
Analysis of PDEs
2017-05-23 v2 Differential Geometry
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.
Cite
@article{arxiv.1509.02645,
title = {Inverse problems for the connection Laplacian},
author = {Yaroslav Kurylev and Lauri Oksanen and Gabriel P. Paternain},
journal= {arXiv preprint arXiv:1509.02645},
year = {2017}
}