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Stability of Determination of Riemann Surface from its Dirichlet-to-Neumann Map in Terms of Teichmüller Distance
Dmitrii V. Korikov, Mikhail I. Belishev
Source abstract
Abstract. As is known, the Dirichlet-to-Neumann operator [Formula: see text] of a Riemannian surface [Formula: see text] determines the surface up to conformal equivalence class [Formula: see text]. Such classes constitute the Teichmüller space with the distance [Formula: see text]. We show that the determination is continuous: [Formula: see text] implies [Formula: see text].
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