A Uniform Poincaré Estimate for Quadratic Differentials on Closed Surfaces
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چکیده
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.
منابع مشابه
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تاریخ انتشار 2013