English

Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem

Differential Geometry 2024-10-11 v2 Analysis of PDEs

Abstract

We study the scattering rigidity problem in Lorentzian geometry: recovery of a Lorentzian metric from the scattering relation known on a lateral timelike boundary. We show that one can recover the jet of the metric up to a gauge transformation near a lightlike strictly convex point. Assuming that the metric is real analytic, we show that one can recover the metric up to a gauge transformation as well near such a point.

Keywords

Cite

@article{arxiv.2404.15541,
  title  = {Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem},
  author = {Plamen Stefanov},
  journal= {arXiv preprint arXiv:2404.15541},
  year   = {2024}
}