论文标题
双曲线空间中具有毛细管边界的紧凑型高空的刚度结果
Some rigidity results on compact hypersurfaces with capillary boundary in Hyperbolic space
论文作者
论文摘要
在本文中，我们证明了在双曲线空间中各种超曲面上支撑的毛细血管高空面积的Heintze-Karcher型不平等。平等案例仅发生在完全脐带曲面上。然后，我们应用此结果来证明Alexandrov类型定理用于双曲线空间中的嵌入式毛细血管超曲面。此外，我们证明了在$ \ Mathbb b^{n+1} _+$中支持的毛细血管超曲面的其他刚度结果。
In this paper, we prove a Heintze-Karcher type inequality for capillary hypersurfaces supported on various hypersurfaces in the hyperbolic space. The equality case only occurs on capillary totally umbilical hypersurfaces. Then we apply this result to prove the Alexandrov type theorem for embedded capillary hypersurfaces in the hyperbolic space. In addition, we prove some other rigidity results for capillary hypersurfaces supported on totally geodesic plane in $\mathbb B^{n+1}_+$.
