Extremal Area of Polygons, sliding along a Circle

Fuente: arXiv
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Main Author: Siersma, Dirk
Format: Preprint
Published: 2020
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author Siersma, Dirk
author_facet Siersma, Dirk
contents We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. In the even dimensional case non-isolated singularities occur as `zigzag trains'.
format Preprint
id arxiv_https___arxiv_org_abs_2001_10882
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Extremal Area of Polygons, sliding along a Circle
Siersma, Dirk
Metric Geometry
Geometric Topology
58K05, 52B99
We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. In the even dimensional case non-isolated singularities occur as `zigzag trains'.
title Extremal Area of Polygons, sliding along a Circle
topic Metric Geometry
Geometric Topology
58K05, 52B99
url https://arxiv.org/abs/2001.10882