Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces
Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces
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DOI：
10.1016/j.aim.2019.05.023
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发表时间：
2018-02
影响因子：
1.7
通讯作者：
C. Bellettini;Otis Chodosh;Neshan Wickramasekera
中科院分区：
文献类型：
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作者：
C. Bellettini;Otis Chodosh;Neshan Wickramasekera
弱稳定常平均曲率 (CMC) 超曲面是关于体积保持变形的面积函数的稳定临界点。我们为弱稳定 CMC 超曲面建立了点曲率估计（在非奇异维度）和片状定理（在所有维度），给出了第一和第三作者最近工作中建立的弱稳定 CMC 超曲面紧性定理的有效版本 [6]。我们的结果推广了 Schoen-Simon-Yau 和 Schoen-Simon 分别证明的强稳定超曲面的曲率估计和片状定理。
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.