Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces

Costante Bellettini, Otis Chodosh, Neshan Wickramasekera

Research output: Contribution to journalArticle

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 [6]. Our results generalize the curvature estimate and the sheeting theorem proven respectively by Schoen–Simon–Yau and Schoen–Simon for strongly stable hypersurfaces.

Original languageEnglish (US)
Pages (from-to)133-157
Number of pages25
JournalAdvances in Mathematics
Volume352
DOIs
StatePublished - Aug 20 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Constant mean curvature
  • Curvature estimates
  • Sheeting theorems
  • Weak stability

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