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Title: Rigidity in the Lorentzian Calderón problem with formally determined data
We study the Lorentzian Calderón problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This problem is a wave equation analogue of the Calderón problem on Riemannian manifolds. We prove that if a globally hyperbolic metric agrees with the Minkowski metric outside a compact set and has the same hyperbolic Dirichlet-to-Neumann map as the Minkowski metric, then it must be the Minkowski metric up to diffeomorphism. In fact this follows from a stronger result that solves a formally determined inverse problem with a much smaller amount of measurements. To prove these results we introduce a new method for geometric hyperbolic inverse problems. The method is based on distorted plane wave solutions and on a combination of geometric, topological and unique continuation arguments.  more » « less
Award ID(s):
2307800 1908391
PAR ID:
10709897
Author(s) / Creator(s):
; ;
Publisher / Repository:
AMS
Date Published:
Journal Name:
Communications of the American Mathematical Society
Volume:
6
Issue:
14
ISSN:
2692-3688
Page Range / eLocation ID:
749 to 792
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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