Stability of Capillary Hypersurfaces with Planar Boundaries

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• 作者：Haizhong Li ; Changwei Xiong
• 关键词：Capillary hypersurfaces ; Stability ; Planar boundary
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：79-94
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

We prove that, in a Euclidean domain bounded by hyperplanes having linearly independent normals, a connected oriented compact immersed stable capillary hypersurface \(M^n\) disjoint from the edges of the domain and with the contact angles belonging to \([\pi /2,\pi ]\) must be part of a sphere, if \(\partial M\) is embedded for \(n=2\), or \(\partial M\) is convex in the hyperplane for \(n\ge 3\). By applying a similar argument, we also discuss two other cases where a stable capillary hypersurface must be part of a sphere.