Standard

How many times can the volume of a convex polyhedron be increased by isometric deformations? / Alexandrov, Victor.

в: Beitrage zur Algebra und Geometrie, Том 58, № 3, 01.09.2017, стр. 549-554.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Alexandrov, V 2017, 'How many times can the volume of a convex polyhedron be increased by isometric deformations?', Beitrage zur Algebra und Geometrie, Том. 58, № 3, стр. 549-554. https://doi.org/10.1007/s13366-017-0336-8

APA

Alexandrov, V. (2017). How many times can the volume of a convex polyhedron be increased by isometric deformations? Beitrage zur Algebra und Geometrie, 58(3), 549-554. https://doi.org/10.1007/s13366-017-0336-8

Vancouver

Alexandrov V. How many times can the volume of a convex polyhedron be increased by isometric deformations? Beitrage zur Algebra und Geometrie. 2017 сент. 1;58(3):549-554. doi: 10.1007/s13366-017-0336-8

Author

Alexandrov, Victor. / How many times can the volume of a convex polyhedron be increased by isometric deformations?. в: Beitrage zur Algebra und Geometrie. 2017 ; Том 58, № 3. стр. 549-554.

BibTeX

@article{cd74c4ce3878450c965caa280d137251,
title = "How many times can the volume of a convex polyhedron be increased by isometric deformations?",
abstract = "We prove that the answer to the question of the title is {\textquoteleft}as many times as you want.{\textquoteright} More precisely, given any constant c> 0 , we construct two oblique triangular bipyramids, P and Q, in Euclidean 3-space, such that P is convex, Q is nonconvex and intrinsically isometric to P, and vol Q> c· vol P> 0.",
keywords = "Bipyramid, Convex polyhedron, Euclidean space, Intrinsic isometry, Intrinsic metric, Volume increasing deformation",
author = "Victor Alexandrov",
year = "2017",
month = sep,
day = "1",
doi = "10.1007/s13366-017-0336-8",
language = "English",
volume = "58",
pages = "549--554",
journal = "Beitrage zur Algebra und Geometrie",
issn = "0138-4821",
publisher = "Springer Berlin",
number = "3",

}

RIS

TY - JOUR

T1 - How many times can the volume of a convex polyhedron be increased by isometric deformations?

AU - Alexandrov, Victor

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We prove that the answer to the question of the title is ‘as many times as you want.’ More precisely, given any constant c> 0 , we construct two oblique triangular bipyramids, P and Q, in Euclidean 3-space, such that P is convex, Q is nonconvex and intrinsically isometric to P, and vol Q> c· vol P> 0.

AB - We prove that the answer to the question of the title is ‘as many times as you want.’ More precisely, given any constant c> 0 , we construct two oblique triangular bipyramids, P and Q, in Euclidean 3-space, such that P is convex, Q is nonconvex and intrinsically isometric to P, and vol Q> c· vol P> 0.

KW - Bipyramid

KW - Convex polyhedron

KW - Euclidean space

KW - Intrinsic isometry

KW - Intrinsic metric

KW - Volume increasing deformation

UR - http://www.scopus.com/inward/record.url?scp=85027060164&partnerID=8YFLogxK

U2 - 10.1007/s13366-017-0336-8

DO - 10.1007/s13366-017-0336-8

M3 - Article

AN - SCOPUS:85027060164

VL - 58

SP - 549

EP - 554

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 3

ER -

ID: 9966560