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.
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}
}