Sharp distortion growth for bilipschitz extension of planar maps

@article{Kovalev2012SharpDG,
  title={Sharp distortion growth for bilipschitz extension of planar maps},
  author={L. Kovalev},
  journal={Conformal Geometry and Dynamics of The American Mathematical Society},
  year={2012},
  volume={16},
  pages={124-131}
}
  • L. Kovalev
  • Published 2012
  • Mathematics
  • Conformal Geometry and Dynamics of The American Mathematical Society
  • This note addresses the quantitative aspect of the bilipschitz extension problem. The main result states that any bilipschitz embedding of $\mathbb R$ into $\mathbb R^2$ can be extended to a bilipschitz self-map of $\mathbb R^2$ with a linear bound on the distortion. 
    4 Citations
    Symmetrization and extension of planar bi-Lipschitz maps
    • 2
    • PDF
    Radial extension of a bi-Lipschitz parametrization of a starlike Jordan curve
    • 8
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 38 REFERENCES
    Plane sets allowing bilipschitz extensions
    • 10
    • Highly Influential
    Chord-arc surfaces with small constant, I☆
    • 77
    Boundary Behaviour of Conformal Maps
    • 1,458
    ON BOUNDARY CORRESPONDENCE UNDER QUASICONFORMAL MAPPINGS
    • 94
    • PDF
    Lectures on quasiconformal mappings
    • 1,109
    A planar bi-Lipschitz extension theorem
    • 24
    • PDF
    Potential theory in the complex plane
    • 1,096