arXiv:1810.09308 Abstract | arXiv Analytics

arXiv:1810.09308 [math.DG]Abstract References Reviews Resources

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

Published 2018-10-22Version 1

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 $|c|$ away from a point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.

Categories: math.DG, math.DS, math.SG

Subjects: 53C42

Keywords: constant curvature, riemannian surface, curvature equal, regularity

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