在$\mathbb R^d$中，由柔性多面体限定的区域中的拉普拉斯算子的谱在柔性期间并不总是保持不变
The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flex
摘要：
受柔性多面体理论的启发，本文研究了欧氏$d$ -空间中特殊有界区域上Laplace算子的Dirichlet和Neumann特征值.这种域的边界是允许连续变形（挠曲）的嵌入式单纯复形，在该连续变形下，复形的每个单纯形作为固体移动，并且域的空间形状的改变仅通过改变二面角来实现。本文的主要结果是，在这样的区域的拉普拉斯算子的Dirichlet和Neumann谱不一定保持不变，在其边界的伸缩。
英文摘要：
Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows a continuous deformation (a flex), under which each simplex of the complex moves as a solid body and the change in the spatial shape of the domain is achieved through a change of the dihedral angles only. The main result of this article is that both the Dirichlet and Neumann spectra of the Laplace operator in such a domain do not necessarily remain unaltered during the flex of its boundary.
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