单位2-球面上具有自由边界的Delaunay曲面
Delaunay surfaces with free boundary on the unit $2$-sphere
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中文总结 AI 辅助
本研究刻画与单位球正交相交的常平均曲率对称嵌入旋转曲面，证明单位球内外各存在1个常平均曲率为-1的自由边界纽结面，且不存在常平均曲率为1的此类曲面。
中文摘要 AI 辅助
我们刻画了所有与单位球正交相交的、具有常平均曲率的对称嵌入旋转曲面。众所周知，单位球内部存在唯一的自由边界悬链面。通过类比，我们证明单位球内部存在唯一的自由边界纽结面，其常平均曲率等于-1；此外，单位球外部还存在唯一的紧致自由边界纽结面，其常平均曲率同样等于-1。然而，不存在与单位球正交相交且常平均曲率为1的对称旋转曲面。
英文摘要
We characterize all symmetric, embedded surfaces of revolution with constant mean curvature that meet the unit sphere orthogonally. It is well known that there exists a unique free boundary catenoid inside of the unit ball. By analogy, we prove the existence of a unique free boundary nodoid inside of the unit ball with constant mean curvature equal to $-1$. Moreover, there exists a unique compact free boundary nodoid \emph{outside} of the unit ball with constant mean curvature equal to $-1$. However, there exists no symmetric surface of revolution with constant mean curvature $1$ that meets the unit sphere orthogonally.
