论文标题
具有Legendrian毛细管边界的最小拉格朗日表面的刚性定理
Rigidity theorems for minimal Lagrangian surfaces with Legendrian capillary boundary
论文作者
论文摘要
在本说明中，我们在$ \ mathbb {s}^3 $上研究了$ \ mathbb {b}^4 $中的最小拉格朗日表面。一方面，我们证明了$ \ mathbb {b}^4 $中的任何最小拉格朗日表面在$ \ mathbb {s}^3 $上都必须是赤道平面磁盘。另一方面，我们证明了$ \ mathbb {b}^4 $中的任何环类型的Lagrangian表面与Legendrian毛细管边界上的$ \ Mathbb {s}^3 $都必须与Lagrangian catenoids之一。这些结果证实了Li，Wang和Weng（Sci。Math。，2020）提出的猜想。
In this note, we study minimal Lagrangian surfaces in $\mathbb{B}^4$ with Legendrian capillary boundary on $\mathbb{S}^3$. On the one hand, we prove that any minimal Lagrangian surface in $\mathbb{B}^4$ with Legendrian free boundary on $\mathbb{S}^3$ must be an equatorial plane disk. One the other hand, we show that any annulus type minimal Lagrangian surface in $\mathbb{B}^4$ with Legendrian capillary boundary on $\mathbb{S}^3$ must be congruent to one of the Lagrangian catenoids. These results confirm the conjecture proposed by Li, Wang and Weng (Sci. China Math., 2020).
