Conformal Gauss Map Geometry and Application to Willmore Surfaces in Model Spaces

Marqué, Nicolas

doi:10.1007/s11118-020-09825-9

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Correspondance1

Conformal Gauss Map1

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2023

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Cited by 2 publications

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“…The correspondance Conf(S 3 ) ≃ SO(4, 1) is known for a long time, see for instance [1,11]. The explicit computations can be found in [21]. There is an isomorphism ϕ : Conf(S 3 ) → SO(4, 1) given by the following relations, where we identify…”

Section: Correspondancementioning

confidence: 99%

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Energy quantization of Willmore surfaces at the boundary of the moduli space

Laurain¹,

Rivière²

2018

Duke Math. J.

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We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. We notably exhibit a new residue which quantifies the potential loss of energy in collar regions. Thanks to these residues, we also establish the compactness (modulo the action of the Möbius group of conformal transformations of R 3 ∪ {∞}) of the space of Willmore immersions of any arbitrary closed 2-dimensional oriented manifold into R 3 with uniformly bounded conformal class and energy below 12π.

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Section: Correspondancementioning

confidence: 99%

“…An introduction to conformal Gauss map can be found in [10,11,21]. Here we sketch the construction and recall the main properties.…”

Section: Conformal Gauss Mapmentioning

confidence: 99%