论文标题
根据Teichmüller距离从其DN-MAP确定Riemann表面的稳定性
Stability of determination of Riemann surface from its DN-map in terms of Teichmüller distance
论文作者
论文摘要
众所周知，Riemannian Surface $（m，g）$的Dirichlet到Neumann运算符$λ$确定表面的结构等效类别$ [（M，G）] $。此类类构成Teichmüller空间，距离$ {\ rm d} _t $。我们表明确定是连续的：$ \ |λ-λ'\ | _ {h^1（\ partial m）\ to l_2（\ partial m）} \ 0 $ to to to 0 $ insuie $ {\ rm d} _t _t _t（[（m，g）]，[（m'，g'，g'，g''））
As is known, the Dirichlet-to-Neumann operator $Λ$ of a Riemannian surface $(M,g)$ determines the surface up to conformal equivalence class $[(M,g)]$. Such classes constitute the Teichmüller space with the distance ${\rm d}_T$. We show that the determination is continuous: $\|Λ-Λ'\|_{H^1(\partial M)\to L_2(\partial M)}\to 0$ implies ${\rm d}_T([(M,g)],[(M',g')])\to 0$.
