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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Stefanov, Plamen
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912065835237376
author Stefanov, Plamen
author_facet Stefanov, Plamen
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2404_15541
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem
Stefanov, Plamen
Differential Geometry
Analysis of PDEs
35R30, 53C24, 53B30
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.
title Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem
topic Differential Geometry
Analysis of PDEs
35R30, 53C24, 53B30
url https://arxiv.org/abs/2404.15541