On the existence of closed \(C^{1, 1}\) curves of constant curvature

DOI10.1007/s00526-023-02584-6zbMath1527.53002arXiv1810.09308OpenAlexW2897059155MaRDI QIDQ6073862

Yevgeny Liokumovich, Daniel Ketover

Publication date: 12 October 2023

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09308

zbMATH Keywords

curves of constant curvature

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Curves in Euclidean and related spaces (53A04)

Related Items (1)

The first width of non-negatively curved surfaces with convex boundary

Cites Work

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• Closed magnetic geodesics on \(S^2\)
• Embedded constant-curvature curves on convex surfaces
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• Simple closed geodesics on convex surfaces
• Shortening embedded curves
• Min-max theory for networks of constant geodesic curvature
• Min-max theory for constant mean curvature hypersurfaces
• Alexandrov-embedded closed magnetic geodesics on S²
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Degree Theory of Immersed Hypersurfaces

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