Symplectically convex and symplectically star-shaped curves: a variational problem

DOI10.1007/s11784-022-00931-2zbMath1486.49068arXiv2012.14797OpenAlexW3113538751MaRDI QIDQ2124783

Peter Albers, Sergei Tabachnikov

Publication date: 11 April 2022

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.14797

zbMATH Keywords

symplectic spaceinfinitesimal rigidityaffine isoperimetric inequalitysymplectically convexsymplectically star-shaped curves

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Symplectic geometry, contact geometry (53D99) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25) Curves in Euclidean and related spaces (53A04) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30) Affine differential geometry (53A15) Manifolds and measure-geometric topics (49Q99)

Uses Software

• Mathematica

Cites Work

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• Planar \textit{p}-elastic curves and related generalized complete elliptic integrals
• On affine plane curve evolution
• On the Lambert \(w\) function
• Hamiltonian flows on the space of star-shaped curves
• Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves
• A gradient flow for the \(p\)-elastic energy defined on closed planar curves
• The geometry of spherical curves and the algebra of quaternions

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