English

Scattering data versus lens data on surfaces

Differential Geometry 2015-08-14 v1

Abstract

The scattering data of a Riemannian manifold with boundary record the incoming and outgoing directions of each geodesic passing through. We show that the scattering data of a generic Riemannian surface with no trapped geodesics and no conjugate points determine the lengths of geodesics. Counterexamples exists when trapped geodesics are allowed.

Keywords

Cite

@article{arxiv.1508.03081,
  title  = {Scattering data versus lens data on surfaces},
  author = {Christopher B. Croke and Haomin Wen},
  journal= {arXiv preprint arXiv:1508.03081},
  year   = {2015}
}
R2 v1 2026-06-22T10:32:35.220Z