Elastic curves and Willmore Hopf-Tori

More documents

Recommendations

Info

Whitham deformation The moduli space of closed wavelike elastic <strong>curves</strong> in S 2 .Figure:Orbit-like example with orbit-like elastic profile curve.
Whitham deformation The moduli space of closed wavelike elastic <strong>curves</strong> in S 2 .Constrained elastica on S 2 arise from anti-twisted polynomialKilling fields of degree 3:( )iA BX =−B ∗ −iAwhereA = 1 2 (m 2 − κ 2 )λ + λ 3B = −(κ ′′ + 1 2 κ3 − 1 2 m 2κ) + iκ ′ λ + κλ 2 .The branchpoints of the spectral curve are the zeros ofwhere the curvature κ satisfiesdet X = m 6 + m 4 λ 2 + m 2 λ 4 + λ 6κ ′ 2 +14 κ4 − 1 2 m 2κ 2 + 2 √ m 6 κ + 1 4 m2 2 − m 4 = 0 .
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 26 and 27: Whitham deformation The moduli spac
Page 28 and 29: Moduli space of constrained elastic
Page 30 and 31: Moduli space of constrained elastic
Page 32: Moduli space of constrained elastic

Elastic curves and Willmore Hopf-Tori

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?