The linearization of the boundary rigidity problem for MP-systems and generic local boundary rigidity
Sebastián Muñoz-Thon · Inverse Problems · 2024
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 Dairbekov et al (2007 Adv. Math. 216 535–609) 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 be k-gauge equivalent.