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

в: Journal of Geometry, Том 111, № 2, 32, 03.06.2020.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

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@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",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
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

N1 - Publisher Copyright: © 2020, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

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