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The Minimax Sphere Eversion

In: Visualization and Mathematics

Author

Listed:
  • George Francis

    (University of Illinois, Mathematics Dept.)

  • John M. Sullivan

    (University of Minnesota, Mathematics Dept.)

  • Rob B. Kusner

    (University of Massachusetts, Mathematics Dept.)

  • Ken A. Brakke

    (Susquehanna University, Mathematics Dept.)

  • Chris Hartman

    (University of Illinois, Mathematics Dept.)

  • Glenn Chappell

    (University of Illinois, Mathematics Dept.)

Abstract

Summary We consider an eversion of a sphere driven by a gradient flow for elastic bending energy. We start with a halfway model which is an unstable Willmore sphere with 4-fold orientation-reversing rotational symmetry. The regular homotopy is automatically generated by flowing down the gradient of the energy from the halfway model to a round sphere, using the Surface Evolver. This flow is not yet fully understood; however, our numerical simulations give evidence that the resulting eversion is isotopic to one of Morin’s classical sphere eversions. These simulations were presented as real-time interactive animations in the CAVE TM automatic virtual environment at Supercomputing’95, as part of an experiment in distributed, parallel computing and broad-band, asynchronous networking.

Suggested Citation

  • George Francis & John M. Sullivan & Rob B. Kusner & Ken A. Brakke & Chris Hartman & Glenn Chappell, 1997. "The Minimax Sphere Eversion," Springer Books, in: Hans-Christian Hege & Konrad Polthier (ed.), Visualization and Mathematics, pages 3-20, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59195-2_1
    DOI: 10.1007/978-3-642-59195-2_1
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