Boundary rigidity and stability for generic simple metrics

  title={Boundary rigidity and stability for generic simple metrics},
  author={Plamen Stefanov and Gunther Uhlmann},
We study the boundary rigidity problem for compact Riemannian manifolds with boundary (M,g): is the Riemannian metric g uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function ρg(x, y) known for all boundary points x and y? We prove in this paper local and global uniqueness and stability for the boundary rigidity problem for generic simple metrics. More specifically, we show that there exists a generic set G of simple Riemannian metrics such that for… CONTINUE READING
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