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A uniform Poincaré estimate for quadratic differentials on closed surfaces

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Abstract

We revisit the classical Poincaré inequality on closed surfaces, and prove its natural analogue for quadratic differentials. In stark contrast to the classical case, our inequality does not degenerate when we work on hyperbolic surfaces that themselves are degenerating, and this fact turns out to be essential for applications to the Teichmüller harmonic map flow.

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Acknowledgments

Partially supported by The Leverhulme Trust and EPSRC Grant number EP/K00865X/1.

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Authors and Affiliations

  1. Mathematics Institute, University of Leipzig, Augustusplatz 10, 04109 , Leipzig, Germany

    Melanie Rupflin

  2. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Peter Topping

Authors
  1. Melanie Rupflin
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  2. Peter Topping
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Correspondence to Melanie Rupflin.

Additional information

Communicated by J. Jost.

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Rupflin, M., Topping, P. A uniform Poincaré estimate for quadratic differentials on closed surfaces. Calc. Var. 53, 587–604 (2015). https://doi.org/10.1007/s00526-014-0759-0

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  • DOI: https://doi.org/10.1007/s00526-014-0759-0

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