Isoperimetric Inequalities for Immersed Closed Spherical Curves

@inproceedings{Weiner2010IsoperimetricIF,
  title={Isoperimetric Inequalities for Immersed Closed Spherical Curves},
  author={Joel L. Weiner},
  year={2010}
}
Let a: Sl ->S2 be a C2 immersion with length L and total curvature K . If a is regularly homotopic to a circle traversed once then L2 + K2 > 4n2 with equality if and only if a is a circle traversed once. If a has nonnegative geodesic curvature and multiple points then L + K > An with equality if and only if a is a great circle traversed twice. 

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