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Area-perimeter duality in polygon spaces. / Khimshiashvili, Giorgi; Panina, Gaiane; Siersma, Dirk.

In: Mathematica Scandinavica, Vol. 127, No. 2, 01.08.2021, p. 252-263.

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

Harvard

Khimshiashvili, G, Panina, G & Siersma, D 2021, 'Area-perimeter duality in polygon spaces', Mathematica Scandinavica, vol. 127, no. 2, pp. 252-263. https://doi.org/10.7146/math.scand.a-126041

APA

Khimshiashvili, G., Panina, G., & Siersma, D. (2021). Area-perimeter duality in polygon spaces. Mathematica Scandinavica, 127(2), 252-263. https://doi.org/10.7146/math.scand.a-126041

Vancouver

Khimshiashvili G, Panina G, Siersma D. Area-perimeter duality in polygon spaces. Mathematica Scandinavica. 2021 Aug 1;127(2):252-263. https://doi.org/10.7146/math.scand.a-126041

Author

Khimshiashvili, Giorgi ; Panina, Gaiane ; Siersma, Dirk. / Area-perimeter duality in polygon spaces. In: Mathematica Scandinavica. 2021 ; Vol. 127, No. 2. pp. 252-263.

BibTeX

@article{c7260625972c48dfa8bceb6e26e54a7a,
title = "Area-perimeter duality in polygon spaces",
abstract = "Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.",
author = "Giorgi Khimshiashvili and Gaiane Panina and Dirk Siersma",
year = "2021",
month = aug,
day = "1",
doi = "10.7146/math.scand.a-126041",
language = "English",
volume = "127",
pages = "252--263",
journal = "Mathematica Scandinavica",
issn = "0025-5521",
publisher = "Mathematica Scandinavica",
number = "2",

}

RIS

TY - JOUR

T1 - Area-perimeter duality in polygon spaces

AU - Khimshiashvili, Giorgi

AU - Panina, Gaiane

AU - Siersma, Dirk

PY - 2021/8/1

Y1 - 2021/8/1

N2 - Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.

AB - Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.

UR - http://www.scopus.com/inward/record.url?scp=85118993215&partnerID=8YFLogxK

U2 - 10.7146/math.scand.a-126041

DO - 10.7146/math.scand.a-126041

M3 - Article

AN - SCOPUS:85118993215

VL - 127

SP - 252

EP - 263

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

IS - 2

ER -

ID: 126323418