AI 中文总结
本文针对n≥4的情况，证明球Bⁿ中的局部共形平坦自由边界极小超曲面仅为赤道球或临界悬链面，且赤道球是该类中具有Bⁿ⁻¹拓扑的唯一曲面。
AI 中文摘要
在本文中，我们证明对于所有n≥4，Bⁿ中的局部共形平坦自由边界极小超曲面必为赤道球或临界悬链面。由此得出，在Bⁿ中具有Bⁿ⁻¹拓扑的局部共形平坦自由边界极小超曲面里，赤道球是唯一的。
英文摘要
In this note, we show that a locally conformally flat free boundary minimal hypersurface in $B^n$ must be either an equatorial ball or a critical catenoid for all $n \geq 4$. As a consequence, we conclude that the equatorial ball is unique among locally conformally flat free boundary minimal hypersurfaces in $B^n$ with the topology of $B^{n - 1}$.
CommentsSix pages. Comments are welcome!
