Three travel time inverse problems on simple Riemannian manifolds
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- by Joonas Ilmavirta, Boya Liu and Teemu Saksala;
- Proc. Amer. Math. Soc. 151 (2023), 4513-4525
- DOI: https://doi.org/10.1090/proc/16453
- Published electronically: June 23, 2023
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Abstract:
We provide new proofs based on the Myers–Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics.References
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Bibliographic Information
- Joonas Ilmavirta
- Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, FI-40014, Finland
- MR Author ID: 1014879
- ORCID: 0000-0002-2399-0911
- Email: joonas.ilmavirta@jyu.fi
- Boya Liu
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- Email: bliu35@ncsu.edu
- Teemu Saksala
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- MR Author ID: 1277799
- ORCID: 0000-0002-3785-9623
- Email: tssaksal@ncsu.edu
- Received by editor(s): August 17, 2022
- Received by editor(s) in revised form: February 22, 2023
- Published electronically: June 23, 2023
- Additional Notes: The first author was supported by the Academy of Finland (projects 351665 and 351656). The third author was supported by the National Science Foundation under grant DMS-2204997.
- Communicated by: Jiaping Wang
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4513-4525
- MSC (2020): Primary 53C21, 53C24, 53C80, 86A22
- DOI: https://doi.org/10.1090/proc/16453
- MathSciNet review: 4643335