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The Weil–Petersson Visual Sphere

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Abstract

We formulate and describe a visual compactification of the Teichmüller space by Weil–Petersson geodesic rays emanating from a point X. We focus on analogies with Bers’s compactification: due to noncompleteness, finite rays correspond to cusps, and such cusps are dense in the visual sphere. By analogy with a result of Kerckhoff and Thurston, we show the natural action of the mapping class group does not extend continuously to the visual compactification. We conclude with examples that distinguish the visual boundary from Bers’s boundary for Teichmüller space

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Correspondence to Jeffrey F. Brock.

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Research partially supported by NSF Grants DMS 0204454 and 0354288

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Brock, J.F. The Weil–Petersson Visual Sphere. Geom Dedicata 115, 1–18 (2005). https://doi.org/10.1007/s10711-005-4044-4

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  • DOI: https://doi.org/10.1007/s10711-005-4044-4

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