论文标题
使用Weierstrass表示公式的Fraser-LI猜想的新方法
A new approach to the Fraser-Li conjecture with the Weierstrass representation formula
论文作者
论文摘要
在本文中，我们提供了足够的条件，可以通过$ \ mathbb {r}^3 $在表面上的曲线提供足够的条件，可以通过与球体的正交交点给出。该结果使得在处理球$ \ mathbb {b}^3 $中处理自由边界最小表面时，可以完全根据Weierstrass数据完全表达边界条件。此外，我们证明了嵌入式自由边界最小环的高斯图是一对一的。通过使用此功能，可以将Fraser-LI猜想转化为确定高斯图的问题。另一方面，我们表明环环中的liouville型边界价值问题给出了一些新的见解，以了解浸入最小的环形与球的结构。它还提出了针对Fraser-LI猜想的一种新的PDE理论方法。
In this paper, we provide a sufficient condition for a curve on a surface in $\mathbb{R}^3$ to be given by an orthogonal intersection with a sphere. This result makes it possible to express the boundary condition entirely in terms of the Weierstrass data without integration when dealing with free boundary minimal surfaces in a ball $\mathbb{B}^3$. Moreover, we show that the Gauss map of an embedded free boundary minimal annulus is one to one. By using this, the Fraser-Li conjecture can be translated into the problem of determining the Gauss map. On the other hand, we show that the Liouville type boundary value problem in an annulus gives some new insight into the structure of immersed minimal annuli orthogonal to spheres. It also suggests a new PDE theoretic approach to the Fraser-Li conjecture.
