We consider foliations of compact complex manifolds by analytic curves. We suppose that the line bundle tangent to the foliation is negative. We show that, in the generic case, there exists a finitely smooth homomorphism holomorphic on the fibers and mapping fiberwise the manifold of universal coverings over the leaves passing through a given transversal B onto some domain with continuous boundary in B × ℂ depending on the leaves. The problem can be reduced to the study of the Beltrami equation with parameters on the unit disk in the case when the derivatives of the corresponding Beltrami coefficient grow no faster than some negative power of the distance to the boundary of the disk.

中文翻译：

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具有双曲叶和参数的Beltrami方程的​​叶面的一致化

我们通过解析曲线来考虑紧凑型复杂流形的叶面。我们假设与叶面相切的线束为负。我们证明，在一般情况下，纤维上存在全光滑的同态同质性，并通过给定的横向B将叶上的通用覆盖层的流形映射到遍历给定B的某个域上，该域具有B× continuous中的连续边界，具体取决于叶。在相应的Beltrami系数的导数增长速度不快于到磁盘边界的负幂的情况下，可以将问题简化为在带单位圆盘上研究带参数的Beltrami方程。