论文标题
关于不可定向表面的EIT问题
On the EIT problem for nonorientable surfaces
论文作者
论文摘要
令$（ω，g）$是一个平滑的紧凑型二维Riemannian歧管，带有边界，$λ_g：f \ mapsto \partial_νu| _ {\partialΩ} $它的dn地图，其中$ u $ u $ u $ obeys $ obeys $ obeys $ obeys $ ube y $Δ_g= 0 $ = 0 $ in $ ch $ gomω$ and $ω$ | _ _}电阻断层扫描问题是从$λ_g$确定$ω$。 提出了一个标准，该标准能够检测（通过$λ_g$），无论$ω$是否可以定位。 BC方法的代数版本用于解决Moebius频段的EIT问题。主要的仪器是$ m $的双覆盖$ {\ mathbb m} $的全体形态函数的代数，由$λ_g$确定，高于等法同构。它的Gelfand Spectrum（一组字符）扮演着构建相关副本$（m'，g'）$（m，g）$的材料的角色。该副本在共同的等同于原始版本上，提供$ \ partial m'= \ partial m，\，\，\，λ_{g'} =λ_g$，从而解决了问题。
Let $(Ω,g)$ be a smooth compact two-dimensional Riemannian manifold with boundary, $Λ_g: f\mapsto \partial_νu|_{\partialΩ}$ its DN map, where $u$ obeys $Δ_g u=0$ in $Ω$ and $u|_{\partial Ω}=f$. The Electric Impedance Tomography problem is to determine $Ω$ from $Λ_g$. A criterion is proposed that enables one to detect (via $Λ_g$) whether $Ω$ is orientable or not. The algebraic version of the BC-method is applied to solve the EIT problem for the Moebius band. The main instrument is the algebra of holomorphic functions on the double covering ${\mathbb M}$ of $M$, which is determined by $Λ_g$ up to an isometric isomorphism. Its Gelfand spectrum (the set of characters) plays the role of the material for constructing a relevant copy $(M',g')$ of $(M,g)$. This copy is conformally equivalent to the original, provides $\partial M'=\partial M,\,\,Λ_{g'}=Λ_g$, and thus solves the problem.
