On the existence of closed C1,1 curves of constant curvature

On the existence of closed C1,1 curves of constant curvature

We show that on any Riemannian surface for each 0 < c < ∞ there exists an immersed C 1 , 1 curve that is smooth and with curvature equal to ± c away from at most one point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.

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Veröffentlicht in:Calculus of variations and partial differential equations 2023, Vol.62 (9)
Hauptverfasser: Ketover, Daniel, Liokumovich, Yevgeny
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Curvature
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Riemann surfaces
Systems Theory
Theoretical
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Zusammenfassung:We show that on any Riemannian surface for each 0 < c < ∞ there exists an immersed C 1 , 1 curve that is smooth and with curvature equal to ± c away from at most one point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02584-6