Generalized Weierstrass formulae, soliton equations and Willmore surfaces. I. Tori of revolution and the mKdV equation

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dc.creatorKonopelchenko, B. G.
dc.creatorTaimanov, I. A.
dc.date1995-06-29
dc.date.accessioned2026-07-07T09:12:34Z
dc.date.available2026-07-07T09:12:34Z
dc.descriptionA new approach is proposed for study structure and properties of the total squared mean curvature $W$ of surfaces in ${\bf R}^3$. It is based on the generalized Weierstrass formulae for inducing surfaces. The quantity $W$ (Willmore functional) is shown to be invariant under the modified Novikov--Veselov hierarchy of integrable flows. The $1+1$--dimensional case and, in particular, Willmore tori of revolution, are studied in details. The Willmore conjecture is proved for the mKDV--invariant Willmore tori.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/dg-ga/9506011
dc.identifierhttp://arxiv.org/abs/dg-ga/9506011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152060
dc.subjectDifferential Geometry
dc.titleGeneralized Weierstrass formulae, soliton equations and Willmore surfaces. I. Tori of revolution and the mKdV equation
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