We study compact hyperbolic surface laminations. These are a generalization of closed hyperbolic surfaces which appear to be more suited to the study of Teichmuller theory than arbitrary non-compact surfaces. We show that the Teichmuller space of any non-trivial hyperbolic surface lamination is infinite dimensional. In order to prove this result, we study the theory of deformations of hyperbolic surfaces, and we derive what we believe to be a new formula for the derivative of the length of a simple closed geodesic with respect to the action of grafting. This formula complements those derived by McMullen in [23], in terms of the Weil-Petersson metric, and by Wolpert in [33], for the case of earthquakes.

中文翻译：

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双曲表面叠层的地震和嫁接

我们研究紧凑的双曲表面叠片。这些是闭合双曲曲面的推广，与任意非紧凑曲面相比，它们似乎更适合研究 Teichmuller 理论。我们证明了任何非平凡双曲表面层压的 Teichmuller 空间都是无限维的。为了证明这一结果，我们研究了双曲曲面的变形理论，并推导出了我们认为是简单闭合测地线长度相对于接枝作用的导数的新公式。这个公式补充了 McMullen 在 [23] 中根据 Weil-Petersson 度量和 Wolpert 在 [33] 中针对地震情况得出的那些公式。