On the area of a polygonal linkage

DOI10.1134/S1064562412010401zbMath1243.58009OpenAlexW2025549028MaRDI QIDQ416955

G. N. Khimshiashvili, Gaiane Yu. Panina

Publication date: 10 May 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562412010401

zbMATH Keywords

Morse theorycritical pointpolygonal linkage

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Critical points of functions and mappings on manifolds (58K05)

Related Items (9)

Nondegeneracy of certain constrained extrema ⋮ Cyclic configurations of spherical polygons ⋮ Discrete Morse theory for the moduli spaces of polygonal linkages, or solitaire on a circle ⋮ On the area of constrained polygonal linkages ⋮ Critical configurations of planar multiple penduli ⋮ Polygons with prescribed edge slopes: configuration space and extremal points of perimeter ⋮ Motion planning and control of a planar polygonal linkage ⋮ Oriented area as a Morse function on polygon spaces ⋮ Equivalent cyclic polygon of a euclidean travelling salesman problem tour and modified formulation

Cites Work

• Unnamed Item
• Morse index of a cyclic polygon
• Configuration spaces and signature formulas
• Comments on generalized Heron polynomials and Robbins' conjectures
• Areas of polygons inscribed in a circle
• Homology of planar polygon spaces

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