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 CAVETM automatic virtual environment at Supercomputing’95, as part of an experiment in distributed, parallel computing and broad-band, asynchronous networking.
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Francis, G., Sullivan, J.M., Kusner, R.B., Brakke, K.A., Hartman, C., Chappell, G. (1997). The Minimax Sphere Eversion. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59195-2_1
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DOI: https://doi.org/10.1007/978-3-642-59195-2_1
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