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Extremal area of polygons sliding along curves

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1-s2.0-S0393044023000384-main.pdf (1.37 MB)

Publication date

2023-05

Authors

Siersma, DirkISNI 0000000116400912

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DOI

https://doi.org/10.1016/j.geomphys.2023.104786

Document Type

Article

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Utrecht University Repository
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Abstract

In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a Morse-theoretic approach, which includes the relation with the topology of the configuration spaces. Moreover the condition for extremal inner area gives rise to a billiard: the symplectic billiard, defined by P. Albers and S. Tabachnikov.

Keywords

Area, Billiard, Critical point, Morse index, Polygons, Mathematical Physics, General Physics and Astronomy, Geometry and Topology

Citation

Siersma, D 2023, 'Extremal area of polygons sliding along curves', Journal of Geometry and Physics, vol. 187, 104786, pp. 1-16. https://doi.org/10.1016/j.geomphys.2023.104786

URI

http://hdl.handle.net/1874/432242