On various Teichm\"uller spaces of a surface of infinite topological type
Athanase Papadopoulos (IRMA), Daniele Alessandrini (IRMA), Lixin Liu,, Weixu Su
TL;DR
This paper proves the completeness of the length spectrum metric on Teichmüller spaces for infinite-type surfaces and compares it with other Teichmüller space models, providing new insights into their relationships.
Contribution
It establishes the completeness of the length spectrum metric for infinite-type surfaces and compares it with quasiconformal and Fenchel-Nielsen models.
Findings
Length spectrum metric is complete on infinite-type surfaces.
Examples illustrating differences between various Teichmüller spaces.
Comparative analysis of length spectrum, quasiconformal, and Fenchel-Nielsen spaces.
Abstract
We show that the length spectrum metric on Teichm\"uller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichm\"uller space with quasiconformal and the Fenchel-Nielsen Teichm\"uller spaces on such surfaces
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows