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arXiv · 1810.09308

On the existence of closed $C^{1,1}$ curves of constant curvature

Daniel Ketover·Yevgeny Liokumovich
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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.

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Daniel Ketover, Yevgeny Liokumovich. 2018-10-22. On the existence of closed $C^{1,1}$ curves of constant curvature. https://arxiv.org/abs/1810.09308

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