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Pré-Publication, Document De Travail Année : 2022

Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications

Résumé

We prove an $\epsilon$-regularity result for the tracefree curvature of a Willmore surface with bounded second fundamental form. For such a surface, we obtain a pointwise control of the tracefree second fundamental form from a small control of its $L^2$-norm.Several applications are investigated. Notably, we derive a gap statement for surfaces of the aforementioned type. We further apply our results to deduce regularity results for conformal minimal spacelike immersions into the de Sitter space $S^{4,1}$.

Dates et versions

hal-03869791 , version 1 (24-11-2022)

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Yann Bernard, Paul Laurain, Nicolas Marque. Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications. 2022. ⟨hal-03869791⟩
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