Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications

Autoren: Yann Bernard, Paul Laurain, Nicolas Marque (2020)

We prove an ϵ-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 L2-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 S4,1.

zur Übersicht der Publikationen