A uniform Poincaré estimate for quadratic differentials on closed surfaces
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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 Classification30F10 30F30 30F45 30F60 32G15 35A23 35J46 53A30 58J05
Partially supported by The Leverhulme Trust and EPSRC Grant number EP/K00865X/1.
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