Abstract In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under somea prioriconditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.
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The Lorentzian Lichnerowicz conjecture for real-analytic, three-dimensional manifolds
Abstract We prove that, for a compact, 3-dimensional, real-analytic, Lorentzian manifold, if the group of conformal transformations does not preserve any metric in the conformal class, then the metric is conformally flat.
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- Award ID(s):
- 2109347
- PAR ID:
- 10524066
- Publisher / Repository:
- de gruyter
- Date Published:
- Journal Name:
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 0075-4102
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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