Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Bellettini, Costante
Chodosh, Otis
Wickramasekera, Neshan
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.
Description
Keywords
Constant mean curvature, Curvature estimates, Sheeting theorems, Weak stability
Journal Title
ADVANCES IN MATHEMATICS
Conference Name
Journal ISSN
0001-8708
1090-2082
1090-2082
Volume Title
352
Publisher
Elsevier BV
Publisher DOI
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Sponsorship
Engineering and Physical Sciences Research Council (EP/K00865X/1)