On the existence of closed $C^{1,1}$ curves of constant curvature
Abstract
We show that on any Riemannian surface for each $0<c<\infty$ there exists an immersed $C^{1,1}$ curve that is smooth and with curvature equal to $\pm c$ away from a point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.09308
 arXiv:
 arXiv:1810.09308
 Bibcode:
 2018arXiv181009308K
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Dynamical Systems;
 Mathematics  Symplectic Geometry;
 53C42
 EPrint:
 14 pages