The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in Rd does not always remain unaltered during the flex

Standard

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in R^d does not always remain unaltered during the flex. / Alexandrov, Victor.

In: Journal of Geometry, Vol. 111, No. 2, 32, 03.06.2020.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{f3282fdaf0ee4257b6acb11e3343f024,

title = "The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in Rd does not always remain unaltered during the flex",

abstract = "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.",

keywords = "Asymptotic behavior of eigenvalues, Dihedral angle, Dirichlet eigenvalue, Flexible polyhedron, Laplace operator, Neumann eigenvalue, Volume, Weyl asymptotic formula for the Laplacian, Weyl{\textquoteright}s law, BELLOWS CONJECTURE, CROSS-POLYTOPES, VOLUME, INVARIANT, HEAT-EQUATION, Weyl's law",

author = "Victor Alexandrov",

year = "2020",

month = jun,

day = "3",

doi = "10.1007/s00022-020-00541-8",

language = "English",

volume = "111",

journal = "Journal of Geometry",

issn = "0047-2468",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

RIS

TY - JOUR

T1 - The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in Rd does not always remain unaltered during the flex

AU - Alexandrov, Victor

PY - 2020/6/3

Y1 - 2020/6/3

N2 - 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.

AB - 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.

KW - Asymptotic behavior of eigenvalues

KW - Dihedral angle

KW - Dirichlet eigenvalue

KW - Flexible polyhedron

KW - Laplace operator

KW - Neumann eigenvalue

KW - Volume

KW - Weyl asymptotic formula for the Laplacian

KW - Weyl’s law

KW - BELLOWS CONJECTURE

KW - CROSS-POLYTOPES

KW - VOLUME

KW - INVARIANT

KW - HEAT-EQUATION

KW - Weyl's law

UR - http://www.scopus.com/inward/record.url?scp=85086043829&partnerID=8YFLogxK

U2 - 10.1007/s00022-020-00541-8

DO - 10.1007/s00022-020-00541-8

M3 - Article

AN - SCOPUS:85086043829

VL - 111

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

IS - 2

M1 - 32

ER -

ID: 24519087