On the Topology of Surfaces with a Common Boundary and Close DN-Maps

Let Ω be a smooth compact Riemann surface with the boundary Γ, and let Λ : H 1 (Γ) ↦ L 2 (Γ), Λf ≔ ∂ ν u| Γ be its DN map, where u obeys Δ g u = 0 in Ω and u = f on Γ. As is known, the genus m of the surface Ω is determined by its DN map Λ. In this paper, we prove the existence of Riemann surfaces o...

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Veröffentlicht in:	Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.283 (4), p.549-555
1. Verfasser:	Korikov, D. V.
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Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Riemann surfaces Topology
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description	Let Ω be a smooth compact Riemann surface with the boundary Γ, and let Λ : H 1 (Γ) ↦ L 2 (Γ), Λf ≔ ∂ ν u\| Γ be its DN map, where u obeys Δ g u = 0 in Ω and u = f on Γ. As is known, the genus m of the surface Ω is determined by its DN map Λ. In this paper, we prove the existence of Riemann surfaces of arbitrary genus m′ > m, with the boundary Γ, and such that their DN maps are arbitrarily close to Λ with respect to the operator norm. In other words, an arbitrarily small perturbation of the DN map may change the surface topology.
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V.</creatorcontrib><title>On the Topology of Surfaces with a Common Boundary and Close DN-Maps</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>Let Ω be a smooth compact Riemann surface with the boundary Γ, and let Λ : H 1 (Γ) ↦ L 2 (Γ), Λf ≔ ∂ ν u\| Γ be its DN map, where u obeys Δ g u = 0 in Ω and u = f on Γ. As is known, the genus m of the surface Ω is determined by its DN map Λ. In this paper, we prove the existence of Riemann surfaces of arbitrary genus m′ > m, with the boundary Γ, and such that their DN maps are arbitrarily close to Λ with respect to the operator norm. 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In this paper, we prove the existence of Riemann surfaces of arbitrary genus m′ > m, with the boundary Γ, and such that their DN maps are arbitrarily close to Λ with respect to the operator norm. In other words, an arbitrarily small perturbation of the DN map may change the surface topology.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10958-024-07291-x</doi><tpages>7</tpages></addata></record>
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title	On the Topology of Surfaces with a Common Boundary and Close DN-Maps
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