The polarization tensor is a geometric quantity associated with a domain. It is a signature of the small inclusion's existence inside a domain and used in the small volume expansion method to reconstruct small inclusions by boundary measurements. In this paper, we consider the question of the polarization tensor vanishing structure of general shape. The only known examples of the polarization tensor vanishing structure are concentric disks and balls. We prove, by the implicit function theorem on Banach spaces, that a small perturbation of a ball can be enclosed by a domain so that the resulting inclusion of the core-shell structure becomes polarization tensor vanishing. The boundary of the enclosing domain is given by a sphere perturbed by spherical harmonics of degree zero and two. This is a continuation of the earlier work \cite{KLS2D} for two dimensions.

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一般形状的极化张量消失结构：小球微扰的存在

极化张量是与域相关的几何量。它是域内小夹杂物存在的标志，用于小体积扩展方法，通过边界测量重建小夹杂物。在本文中，我们考虑了一般形状的极化张量消失结构的问题。极化张量消失结构的唯一已知例子是同心圆盘和球。我们证明，通过巴拿赫空间的隐函数定理，一个小球的微扰可以被一个域包围，从而导致核壳结构的包含成为极化张量消失。封闭域的边界由一个球体给出，球体受到 0 次和 2 次球谐函数的扰动。