Area-perimeter duality in polygon spaces

Fuente: arXiv
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Hauptverfasser: Khimshiashvili, Giorgi, Panina, Gaiane, Siersma, Dirk
Format: Preprint
Veröffentlicht: 2020
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author Khimshiashvili, Giorgi
Panina, Gaiane
Siersma, Dirk
author_facet Khimshiashvili, Giorgi
Panina, Gaiane
Siersma, Dirk
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2002_03146
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Area-perimeter duality in polygon spaces
Khimshiashvili, Giorgi
Panina, Gaiane
Siersma, Dirk
Geometric Topology
52R70, 52B99
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.
title Area-perimeter duality in polygon spaces
topic Geometric Topology
52R70, 52B99
url https://arxiv.org/abs/2002.03146