Elastic curves and Willmore Hopf-Tori

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Moduli space of constrained elasticaFigure: Spectral genus g = 2 constrained wave-like elastic profile curve,and corresponding constrained Willmore-Hopf-torus.
Moduli space of constrained elasticaFigure: Nonembedded example. Spectral genus g = 2 constrainedwave-like elastic profile curve, and corresponding constrainedWillmore-Hopf-torus.
Page 2 and 3: A brief history◮ 1691 J. Bernoull
Page 4 and 5: ◮ If h : S 3 → S 2 is the Hopf-
Page 6 and 7: Figure: A deformation through const
Page 8 and 9: Finite type curves in S 2Curves in
Page 10 and 11: Finite type curves in S 2Reconstruc
Page 12 and 13: Polynomial Killing fields and spect
Page 14 and 15: Polynomial Killing fields and spect
Page 16 and 17: Whitham deformationPolynomials A, B
Page 18 and 19: Whitham deformationIncreasing the s
Page 20 and 21: Whitham deformationExampleThe branc
Page 22 and 23: Whitham deformation Flow of elastic
Page 24 and 25: Whitham deformation The moduli spac
Page 26 and 27: Whitham deformation The moduli spac
Page 28 and 29: Moduli space of constrained elastic
Page 32: Moduli space of constrained elastic

Elastic curves and Willmore Hopf-Tori

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