@article{d395eef631614c1cbe9b267ae9f9ee86,
title = "Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications",
abstract = "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.",
author = "Yann Bernard and Paul Laurain and Nicolas Marque",
note = "Funding Information: Parts of this work were completed while the second and third authors were guests at Monash University under the Robert Bartnik Fellowship funding program. This work was also partially supported by the ANR BLADE-JC ANR- 18-CE40-002. Funding Information: Parts of this work were completed while the second and third authors were guests at Monash University under the Robert Bartnik Fellowship funding program. This work was also partially supported by the ANR BLADE-JC ANR- 18-CE40-002. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.",
year = "2023",
month = feb,
doi = "10.1007/s00205-022-01839-4",
language = "English",
volume = "247",
journal = "Archive for Rational Mechanics and Analysis",
issn = "0003-9527",
publisher = "Springer-Verlag London Ltd.",
number = "1",
}