Stable capillary hypersurfaces in a wedge
Stable capillary hypersurfaces in a wedge
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DOI：
10.2140/pjm.2016.280.1
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发表时间：
2014-05
影响因子：
0.6
通讯作者：
Jaigyoung Choe;Miyuki Koiso
中科院分区：
文献类型：
--
作者：
Jaigyoung Choe;Miyuki Koiso
设$\Sigma$是$\mathbb R^{n+1}$中由两个超平面围成的楔中的紧致浸入稳定毛细超曲面。假设$\Sigma$以恒定的接触角与这两个超平面相交，并且与楔的边缘不相交。证明了如果$\partial \Sigma$对于$n=2$是嵌入的，或者如果$\partial\Sigma$对于$n\geq3$是凸的，那么$\Sigma$是球面的一部分。对于$\Sigma$在$\mathbb R^{n+1}$的半空间中具有连通边界$\partial\Sigma$也是如此。
Let $\Sigma$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. Suppose that $\Sigma$ meets those two hyperplanes in constant contact angles and is disjoint from the edge of the wedge. It is proved that if $\partial \Sigma$ is embedded for $n=2$, or if $\partial\Sigma$ is convex for $n\geq3$, then $\Sigma$ is part of the sphere. And the same is true for $\Sigma$ in the half-space of $\mathbb R^{n+1}$ with connected boundary $\partial\Sigma$.