Bewaard in:
| Hoofdauteurs: | , , , |
|---|---|
| Formaat: | Preprint |
| Gepubliceerd in: |
2020
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| Onderwerpen: | |
| Online toegang: | https://arxiv.org/abs/2012.04435 |
| Tags: |
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Inhoudsopgave:
- In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold $M$ with boundary from the knowledge of the boundary $\partial M,$ the Neumann eigenvalues $λ_j$ and the boundary values of the eigenfunctions $φ_j|_{\partial M}$. We show that this problem has a stable solution with quantitative stability estimates in a class of manifolds with bounded geometry. More precisely, we show that finitely many eigenvalues and the boundary values of corresponding eigenfunctions, known up to small errors, determine a metric space that is close to the manifold in the Gromov-Hausdorff sense. We provide an algorithm to construct this metric space. This result is based on an explicit estimate on the stability of the unique continuation for the wave operator.