Function theoretic characterizations of Weil–Petersson curves

  • Christopher J. Bishop

    Stony Brook University, USA
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Abstract

The Weil–Petersson class is the closure of the smooth closed curves in the Weil–Petersson metric on universal Teichmüller space defined by Takhtajan and Teo. We give some new characterizations of this class of curves and some new proofs of previously known characterizations. In particular, we give a new, more geometric characterization of the conformal weldings of such curves and characterize the curves themselves in terms of Peter Jones’s -numbers.

Cite this article

Christopher J. Bishop, Function theoretic characterizations of Weil–Petersson curves. Rev. Mat. Iberoam. 38 (2022), no. 7, pp. 2355–2384

DOI 10.4171/RMI/1398