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 language | English |
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Pages (from-to) | 252–263 |
Number of pages | 12 |
Journal | Mathematica Scandinavica |
Volume | 127 |
Issue number | 2 |
DOIs | |
Publication status | Published - 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