Bounded geometry with no bounded pants decomposition

Ara Basmajian; Hugo Parlier; Nicholas G. Vlamis

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arXiv · 2106.13406

Bounded geometry with no bounded pants decomposition

Ara Basmajian·Hugo Parlier·Nicholas G. Vlamis

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Abstract

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.

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Ara Basmajian, Hugo Parlier, Nicholas G. Vlamis. 2021-06-25. Bounded geometry with no bounded pants decomposition. https://arxiv.org/abs/2106.13406

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