Boundary rigidity and stability for generic simple metrics

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dc.creatorStefanov, Plamen
dc.creatorUhlmann, Gunther
dc.date2004-08-05
dc.date.accessioned2026-07-07T05:11:04Z
dc.date.available2026-07-07T05:11:04Z
dc.descriptionWe 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 $ρ_g(x,y)$ known for all boundary points $x$ and $y$? We prove in this paper global uniqueness and stability for the boundary rigidity problem for generic simple metrics. More specifically, we show that there exists a generic set $\mathcal{G}$ of simple Riemannian metrics and an open dense set $\mathcal{U}\subset \mathcal{G}\times\mathcal{G}$, such that any two Riemannian metrics in $\mathcal{U}$ having the same distance function, must be isometric. We also prove Hölder type stability estimates for this problem for metrics which are close to a given one in $\mathcal{G}$.
dc.identifierhttps://arxiv.org/abs/math/0408075
dc.identifierhttp://arxiv.org/abs/math/0408075
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72119
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C20
dc.titleBoundary rigidity and stability for generic simple metrics
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