Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces

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 hy...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 352; pp. 133 - 157
Main Authors Bellettini, Costante, Chodosh, Otis, Wickramasekera, Neshan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 20.08.2019
Subjects
Constant mean curvature
Curvature estimates
Sheeting theorems
Weak stability
Curvature estimates
Sheeting theorems
Weak stability
Constant mean curvature
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Summary: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 [6]. Our results generalize the curvature estimate and the sheeting theorem proven respectively by Schoen–Simon–Yau and Schoen–Simon for strongly stable hypersurfaces.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2019.05.023