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},
  pages={427-486}
}
  • Mohammad Ghomi
  • Published 2015
  • Mathematics
  • arXiv: Differential Geometry
  • 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… CONTINUE READING
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    SHOWING 1-10 OF 70 REFERENCES

    A lower estimate for the number of zero-torsion points of a space curve

    • M. C. Romero-Fuster, V. D. Sedykh
    • Beiträge Algebra Geom., 38(1):183–192,
    • 1997
    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Four Vertices of a Convex Space Curve

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Hypersurfaces of constant curvature in space forms

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    On locally convex manifolds

    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    Geometric complexity of embeddings in ℝd

    VIEW 1 EXCERPT