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Đề tài " Two dimensional compact simple Riemannian manifolds are boundary distance rigid "

Chia sẻ: Nguyen Nhi | Ngày: | Loại File: PDF | Số trang:19

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We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction. 1. Introduction and statement of the results Let (M, g) be a compact Riemannian manifold with boundary ∂M . Let dg (x, y) denote the geodesic distance between x and y. The inverse problem we address in this paper is whether we can determine the Riemannian metric g knowing dg (x, y) for any x ∈ ∂M , y ∈ ∂M . ...

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Nội dung Text: Đề tài " Two dimensional compact simple Riemannian manifolds are boundary distance rigid "

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