Determining Lorentzian manifold from non-linear wave observation at a single point

Published 10 Oct 2023 in math.AP | (2310.06925v1)

Abstract: We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of non-linear wave interaction.

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