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}
}