Abstract
In this article, we study \(C^1\) regular curves in the 2-sphere that start and end at given points with given directions, whose tangent vectors are Lipschitz continuous, and their a.e. existing geodesic curvatures have essentially bounds in an open interval. Especially, we show that a \(C^1\) regular curve is such a curve if and only if the infimum of its lower curvature and the supremum of its upper curvature are constrained in the same interval.
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Acknowledgements
A part of this article is included in my PhD thesis. I would like to thank my advisor Nicolau Saldanha for his guidance and great support throughout my PhD studies. I would like to thank an anonymous reviewer for the useful suggestions. I also would like to thank Capes and Faperj for financial support during my graduate studies at PUC-Rio.
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Zhou, C. The Geometry of \(C^1\) Regular Curves in Sphere with Constrained Curvature. J Geom Anal 31, 5974–5987 (2021). https://doi.org/10.1007/s12220-020-00511-1
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DOI: https://doi.org/10.1007/s12220-020-00511-1