We construct a quasiconformally homogeneous hyperbolic Riemann surface—other than the hyperbolic plane—that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact boundary components, we construct a complete hyperbolic metric on the surface that has bounded geometry but does not admit a bounded pants decomposition.

中文翻译：

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有界几何，无界裤子分解

我们构造了一个准共形齐次双曲黎曼曲面（双曲平面除外），它不允许有界裤子分解。此外，给定具有紧凑边界分量的无限类型的连通可定向拓扑表面，我们在具有有界几何形状但不允许有界裤子分解的表面上构造完整的双曲度量。