• Corpus ID: 88518880

Transformations of harmonic bundles and Willmore surfaces

@article{Quintino2011TransformationsOH,
  title={Transformations of harmonic bundles and Willmore surfaces},
  author={{\'A}urea Casinhas Quintino},
  journal={arXiv: Differential Geometry},
  year={2011}
}
  • Á. Quintino
  • Published 30 December 2011
  • Mathematics
  • arXiv: Differential Geometry
Willmore surfaces are the extremals of the Willmore functional (possibly under a constraint on the conformal structure). With the characterization of Willmore surfaces by the (possibly perturbed) harmonicity of the mean curvature sphere congruence [Blaschke, Ejiri, Rigoli, Burstall-Calderbank], a zero-curvature formulation follows [Burstall-Calderbank]. Deformations on the level of harmonic maps prove to give rise to deformations on the level of surfaces, with the definition of a spectral… 

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Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $${\mathcal{W}} = \int H^2$$ under compactly supported infinitesimal
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