In this paper, we extend the construction of pressure metrics to Teichmuller spaces of surfaces with punctures. This construction recovers Thurston's Riemannian metric on Teichmuller spaces. Moreover, we prove the real analyticity and the convexity of Manhattan curves of the finite area type-preserving Fuchsian representations, and thus we obtain several related entropy rigidity results. Lastly, relating the two topics mentioned above, we show that one can derive the pressure metric by varying Manhattan curves.

中文翻译：

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穿孔表面 Teichmüller 空间的压力度量和曼哈顿曲线

在本文中，我们将压力度量的构建扩展到具有穿孔的表面的 Teichmuller 空间。这种构造恢复了 Teichmuller 空间上的 Thurston 黎曼度量。此外，我们证明了有限区域保型Fuchsian表示的曼哈顿曲线的实解析性和凸性，从而获得了几个相关的熵刚性结果。最后，将上述两个主题联系起来，我们表明可以通过改变曼哈顿曲线来推导出压力度量。