Determining Riemannian Manifolds From Nonlinear Wave Observations at a Single Point

Leo Tzou

Determining Riemannian Manifolds From Nonlinear Wave Observations at a Single Point

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arxiv 2102.01841 v3 pith:TSXGWO3Q submitted 2021-02-03 math.AP math.DG

Leo Tzou This is my paper · ORCID

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keywords pointriemanniansinglewavea-priorideterminesdeterminingdifferential

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abstract

We show that on an a-priori unknown Riemannian manifold $(M,g)$, measuring the source-to-solution map for the semilinear wave equation at a single point determines the topological, differential, and geometric structure.

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Inverse Nonlinear Scattering by a Metric
math.AP 2024-11 conditional novelty 7.0 of 10

Nonlinear wave scattering data on a globally hyperbolic Lorentzian spacetime determine the metric up to conformal diffeomorphism.

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