论文标题
与非简单连接的通用叶子的最小双曲线叶的叶拓扑
Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf
论文作者
论文摘要
如果不恰当的（定向）表面满足条件$（\ star）$，则如果它们的孤立末端“由属累积”。我们表明，满足这种情况的每个表面都与最小的codimension叶子的叶子的叶子同构，其封闭的$ 3 $ manifold上的通用叶子不简单地连接。此外，上述结果对于一个可计数的非相表面家族（满足$（\ star）$）的任何处方也是如此：它们可以与上述相同的最小化构叶叶子共存。所有给定的例子都是双曲线叶子，这意味着它们接受了持续负弯曲的叶轮riemannian指标。
A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on a closed $3$-manifold whose generic leaf is not simply connected. Moreover, the above result is also true for any prescription of a countable family of noncompact surfaces (satisfying $(\star)$): they can coexist in the same minimal codimension one foliation as above. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature.
