منابع مشابه
Boundary Rigidity and Holography
We review boundary rigidity theorems assessing that, under appropriate conditions, Riemannian manifolds with the same spectrum of boundary geodesics are isometric. We show how to apply these theorems to the problem of reconstructing a d + 1 dimensional, negative curvature space-time from boundary data associated to two-point functions of high-dimension local operators in a conformal field theor...
متن کاملBoundary Rigidity with Partial Data
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the boundary. We show that one can recover uniquely a conformal factor near a strictly convex point where we have the information. In particular, this implies that we c...
متن کاملBoundary and Lens Rigidity of Finite Quotients
We consider compact Riemannian manifolds (M,∂M, g) with boundary ∂M and metric g on which a finite group Γ acts freely. We determine the extent to which certain rigidity properties of (M,∂M, g) descend to the quotient (M/Γ, ∂/Γ, g). In particular, we show by example that if (M,∂M, g) is boundary rigid then (M/Γ, ∂/Γ, g) need not be. On the other hand, lens rigidity of (M,∂M, g) does pass to the...
متن کاملBoundary and Lens Rigidity of Lorentzian Surfaces
LARS ANDERSSON, MATTIAS DAHL, AND RALPH HOWARD Abstract. Let g be a Lorentzian metric on the plane R2 that agrees with the standard metric g0 = −dx + dy outside a compact set and so that there are no conjugate points along any time-like geodesic of (R2 , g). Then (R2 , g) and (R2 , g0) are isometric. Further, if (M, g) and (M∗, g∗) are two dimensional compact time oriented Lorentzian manifolds ...
متن کاملRecent Progress on the Boundary Rigidity Problem
The boundary rigidity problem consists in determining a compact, Riemannian manifold with boundary, up to isometry, by knowing the boundary distance function between boundary points. In this paper we announce the result of [25] that one can solve this problem for generic simple metrics. Moreover we probe stability estimates for this problem.
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2004
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2004/01/034