Two dimensional compact simple Riemannian manifolds are boundary distance rigid
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🧮 math.AP
math.DG
keywords
boundaryriemanniancompactsimpledeterminedimensionaldistancegeodesics
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We prove that knowing the length of geodesics joining points on the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.
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