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 -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’-régularité pour les immersions de Willmore par un contrôle de l’énergie Willmore locale.
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3464
Keywords: Willmore surfaces, $\varepsilon $-regularity, bubbling
Mot clés : surfaces de Willmore, $\varepsilon $-régularité, arbres de bulles
Marque, Nicolas 1
@article{AIF_2022__72_2_639_0, author = {Marque, Nicolas}, title = {An $\varepsilon $-regularity result with mean curvature control for {Willmore} immersions and application to minimal bubbling.}, journal = {Annales de l'Institut Fourier}, pages = {639--684}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {2}, year = {2022}, doi = {10.5802/aif.3464}, zbl = {07554666}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3464/} }
TY - JOUR AU - Marque, Nicolas TI - An $\varepsilon $-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling. JO - Annales de l'Institut Fourier PY - 2022 SP - 639 EP - 684 VL - 72 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3464/ DO - 10.5802/aif.3464 LA - en ID - AIF_2022__72_2_639_0 ER -
%0 Journal Article %A Marque, Nicolas %T An $\varepsilon $-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling. %J Annales de l'Institut Fourier %D 2022 %P 639-684 %V 72 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3464/ %R 10.5802/aif.3464 %G en %F AIF_2022__72_2_639_0
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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