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Density of specific Strebel points and its consequences

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Abstract

It is a well-known fact that Strebel points (i.e., the equivalence classes of quasiconformal maps satisfying the frame mapping condition of Strebel) are dense in Teichmüller spaces. In various areas, one has to deal with nowhere dense sets in the universal Teichmüller space T, and it is important to knowwhether a given nowhere dense subset E ⊂ T contains the Strebel points and, if so, whether these points are dense in E.

In this paper, we establish that such points are dense in the set of maps with equal Teichmüller and Grunsky norms. This allows us to solve completely several old problems.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Samuel L. Krushkal

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904-4137, USA

    Samuel L. Krushkal

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  1. Samuel L. Krushkal
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Correspondence to Samuel L. Krushkal.

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Krushkal, S.L. Density of specific Strebel points and its consequences. JAMA 110, 271–296 (2010). https://doi.org/10.1007/s11854-010-0007-2

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  • DOI: https://doi.org/10.1007/s11854-010-0007-2

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