Area-perimeter duality in polygon spaces

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2020-02-08 DOI:10.7146/math.scand.a-126041

G. Khimshiashvili, G. Panina, D. Siersma

引用次数: 0

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.

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多边形空间中的面积-周长对偶

考虑了平面多边形构型空间中以面积和周长为导向的两种自然叶片，并对其叶片的拓扑结构进行了较为详细的研究。特别地，确定了叶的同伦群和同伦类型。确定了具有固定面积和周长的多边形空间的同调群。此外，我们将经典等周对偶推广到所有临界点。最后，对多边形空间及其以外的对偶极值问题给出了一些一般性的评述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.