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A uniform Poincaré estimate for quadratic differentials on closed surfaces

  • Melanie Rupflin
  • Peter Topping
Article

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.

Mathematics Subject Classification 

30F10 30F30 30F45 30F60 32G15 35A23 35J46 53A30 58J05 

Notes

Acknowledgments

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of LeipzigLeipzigGermany
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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