Area-perimeter duality in polygon spaces

Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma

Research output: Contribution to journalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)252–263
Number of pages12
JournalMathematica Scandinavica
Volume127
Issue number2
DOIs
Publication statusPublished - 31 Aug 2021

Bibliographical note

Publisher Copyright:
© 2021 Mathematica Scandinavica. All rights reserved.

Funding

Funding Information: ACKNOWLEDGEMENTS. This work is supported by the RFBR grant 20-01- Funding Information: This work is supported by the RFBR grant 20-01-00070. It is our pleasure to acknowledge the hospitality and excellent working conditions of CIRM, Luminy, where this paper was initiated and completed as a ?Research in Pairs? project.

Keywords

  • Mathematics - Geometric Topology
  • 52R70
  • 52B99

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