Weil-Petersson geometry of Teichmüller–Coxeter complex and its finite rank property
نویسنده
چکیده
Resolving the incompleteness of Weil-Petersson metric on Teichmüller spaces by taking metric and geodesic completion results in two distinct spaces, where the Hopf-Rinow theorem is no longer relevant due to the singular behavior of the Weil-Petersson metric. We construct a geodesic completion of the Teichmüller space through the formalism of Coxeter complex with the Teichmüller space as its non-linear nonhomogeneous fundamental domain. We then show that the metric and geodesic completions both satisfy a finite rank property, demonstrating a similarity with the non-compact symmetric spaces of semi-simple
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