by Joonas Ilmavirta, Boya Liu, Teemu Saksala
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.
Reference:
Three travel time inverse problems on simple Riemannian manifolds (Joonas Ilmavirta, Boya Liu, Teemu Saksala), Proceedings of the American Mathematical Society, 2022. (To appear.)
[show abstract]
[hide 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.
[arXiv]
Bibtex Entry:
@article{simple-travel-time,
author = {Joonas Ilmavirta and Boya Liu and Teemu Saksala},
title = {{Three travel time inverse problems on simple Riemannian manifolds}},
month = aug,
year = {2022},
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.},
url={http://users.jyu.fi/~jojapeil/pub/simple-travel-time.pdf},
arxiv = {2208.08422},
journal = {Proceedings of the American Mathematical Society},
note = {To appear.}
}