The Minimax Sphere Eversion

George Francis, John M. Sullivan, Rob B. Kusner, Ken A. Brakke, Chris Hartman and Glenn Chappell
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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.

A chapter in Visualization and Mathematics, 1997, pp 3-20 from Springer

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.

Keywords: Triple Point; Gradient Flow; Pitchfork Bifurcation; Surface Evolver; Round Sphere (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-3-642-59195-2_1

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