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Title: The linearization of the boundary rigidity problem for MP-systems and generic local boundary rigidity
Abstract We consider an MP -system, that is, a compact Riemannian manifold with boundary, endowed with a magnetic field and a potential. On simple MP -systems, we study the MP -ray transform in order to obtain new boundary rigidity results for MP -systems. We show that there is an explicit relation between the MP -ray transform and the magnetic one, which allows us to apply results from Dairbekovet al(2007Adv. Math.216535–609) to our case. Regarding rigidity, we show that there exists a generic set G m of simple MP -systems, which is open and dense, such that any two MP -systems close to an element in it and having the same boundary action function, must bek-gauge equivalent.  more » « less
Award ID(s):
2154489
PAR ID:
10554847
Author(s) / Creator(s):
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Inverse Problems
Volume:
40
Issue:
12
ISSN:
0266-5611
Format(s):
Medium: X Size: Article No. 125008
Size(s):
Article No. 125008
Sponsoring Org:
National Science Foundation
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