An ε-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling.
Annales de l'Institut Fourier, Volume 72 (2022) no. 2, pp. 639-684.

In this paper, we prove a convergence result for sequences of Willmore immersions with simple minimal bubbles. To this end, we replace the total curvature control in the proof of the ε-regularity for Willmore immersions by a control of the local Willmore energy.

Dans cet article, nous montrons une convergence pour des suites d’immersions de Willmore à bulles minimales simples. À cette fin, nous remplaçons le contrôle par la courbure totale dans la preuve de l’ε-régularité pour les immersions de Willmore par un contrôle de l’énergie Willmore locale.

Received:
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Accepted:
Published online:
DOI: 10.5802/aif.3464
Classification: 35J91,  53B25
Keywords: Willmore surfaces, ε-regularity, bubbling
Marque, Nicolas 1

1 Institut Mathématique de Jussieu, Paris VII Bâtiment Sophie Germain Case 7052, 75205 Paris Cedex 13 (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Marque, Nicolas. An $\varepsilon $-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling.. Annales de l'Institut Fourier, Volume 72 (2022) no. 2, pp. 639-684. doi : 10.5802/aif.3464. https://aif.centre-mersenne.org/articles/10.5802/aif.3464/

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