# Boundary torsion and convex caps of locally convex surfaces

@article{Ghomi2015BoundaryTA, title={Boundary torsion and convex caps of locally convex surfaces}, author={Mohammad Ghomi}, journal={arXiv: Differential Geometry}, year={2015} }

We prove that the torsion of any closed space curve which bounds a simply connected locally convex surface vanishes at least 4 times. This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of positively curved disks in Euclidean space. Furthermore, our result generalizes the 4 vertex theorem of Sedykh for convex space curves, and thus constitutes a far reaching extension of the classical 4 vertex theorem. The proof involves studying the arrangement of…

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