Аннотация
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.
Язык оригинала | английский |
---|---|
Номер статьи | 32 |
Число страниц | 14 |
Журнал | Journal of Geometry |
Том | 111 |
Номер выпуска | 2 |
DOI | |
Состояние | Опубликовано - 3 июн 2020 |