Bellettini, C;
Chodosh, O;
Wickramasekera, N;
(2019)
Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces.
Advances in Mathematics
, 352
pp. 133-157.
10.1016/j.aim.2019.05.023.
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Abstract
Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical points of the area functional with respect to volume preserving deformations. We establish a pointwise curvature estimate (in the non-singular dimensions) and a sheeting theorem (in all dimensions) for weakly stable CMC hypersurfaces, giving an effective version of the compactness theorem for weakly stable CMC hypersurfaces established in the recent work of the first and third-named authors. Our results generalize the curvature estimate and the sheeting theorem proven respectively by Schoen--Simon--Yau and Schoen--Simon for strongly stable hypersurfaces.
| Type: | Article |
|---|---|
| Title: | Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.aim.2019.05.023 |
| Publisher version: | https://doi.org/10.1016/j.aim.2019.05.023 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Constant mean curvature, Curvature estimates, Sheeting theorems, Weak stability |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10068803 |
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