On the area of a polygonal linkage
type: Item
instance of: scholarly article
title: On the area of a polygonal linkage
zbMATH Open document ID: 1243.58009
DOI: 10.1134/S1064562412010401
author: Giorgi Khimshiashvili
author: G. Panina
published in: Doklady Mathematics
publication date: 2012-05-10T00:00:00Z
review text: The main purpose of the paper under review is to study the critical points of oriented area regarded as a function on the moduli space of a polygonal linkage. In all cases, the corresponding nongenericity conditions determine some closed sets with empty interior in the parameter space \({\mathbb R}^n_+\). Connections with the electrostatic potential of the system of unit charges located at the vertices of the linkage are also provided in the present paper.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58K05
zbMATH DE Number: 6032819
zbMATH Keywords: Morse theory
zbMATH Keywords: critical point
zbMATH Keywords: polygonal linkage
MaRDI profile type: Publication
cites work: Q3994637
cites work: Comments on generalized Heron polynomials and Robbins' conjectures
cites work: Homology of planar polygon spaces
cites work: Configuration spaces and signature formulas
cites work: Morse index of a cyclic polygon
cites work: Areas of polygons inscribed in a circle
full work available at URL: s1064562412010401
OpenAlex ID: W2025549028
description: scientific article; zbMATH DE number 6032819