论文标题
自由边界最小的环形浸入单元球中
Free boundary minimal annuli immersed in the unit ball
论文作者
论文摘要
我们构建了一个沉浸在单位球$ \ mathbb {b}^3 $ of $ \ mathbb {r}^3 $中的紧凑型边界最小的annuli家族，除关键catenoid以外的第一个此类示例。这解决了Nitsche在1985年提出的问题。相对于两个正交平面和围绕轴的有限旋转，它们是对称的，并由球形曲率线叶散落。我们表明，嵌入在$ \ mathbb {b}^3 $中的唯一自由边界的最小环形是由球形曲率线散发的，是关键的catenoid；特别是，我们构造的最小环境没有嵌入。另一方面，我们还构建了$ \ mathbb {b}^3 $中的非旋转紧凑型嵌入式毛细血管最小的annuli家族。它们的存在解决了否定的问题，即Wente在1995年提出的问题。
We construct a family of compact free boundary minimal annuli immersed in the unit ball $\mathbb{B}^3$ of $\mathbb{R}^3$, the first such examples other than the critical catenoid. This solves a problem formulated by Nitsche in 1985. These annuli are symmetric with respect to two orthogonal planes and a finite group of rotations around an axis, and are foliated by spherical curvature lines. We show that the only free boundary minimal annulus embedded in $\mathbb{B}^3$ foliated by spherical curvature lines is the critical catenoid; in particular, the minimal annuli that we construct are not embedded. On the other hand, we also construct families of non-rotational compact embedded capillary minimal annuli in $\mathbb{B}^3$. Their existence solves in the negative a problem proposed by Wente in 1995.
