Determining Riemannian Manifolds From Nonlinear Wave Observations at a Single Point
Analysis of PDEs
2021-06-23 v3 Differential Geometry
Abstract
We show that on an a-priori unknown Riemannian manifold , measuring the source-to-solution map for the semilinear wave equation at a single point determines the topological, differential, and geometric structure.
Keywords
Cite
@article{arxiv.2102.01841,
title = {Determining Riemannian Manifolds From Nonlinear Wave Observations at a Single Point},
author = {Leo Tzou},
journal= {arXiv preprint arXiv:2102.01841},
year = {2021}
}
Comments
Updated introduction and references to reflect current state of this problem