TY - JOUR
AU - Uhlmann, Gunther
AB - On a time-oriented Lorentzian manifold (M, g) with nonempty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets S ⊂ M of sources is uniquely determined by measurements of the intersection of future light cones from points in S with a fixed open subset of the boundary of M; here, light rays are reflected at ∂M according to Snell’s law. Our proof is constructive, and allows for interior conjugate points as well as multiply reflected and self-intersecting light cones.
TI - Reconstruction of Lorentzian Manifolds from Boundary Light Observation Sets
JF - International Mathematics Research Notices
DO - 10.1093/imrn/rnx320
DA - 2019-11-18
UR - https://www.deepdyve.com/lp/oxford-university-press/reconstruction-of-lorentzian-manifolds-from-boundary-light-observation-bwVHmgTtyM
SP - 6949
EP - 6987
VL - 2019
IS - 22
DP - DeepDyve
ER -