A uniform Poincare estimate for quadratic differentials on closed surfaces

Rupflin, Melanie; Topping, Peter M.

doi:10.1007/s00526-014-0759-0

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A uniform Poincare estimate for quadratic differentials on closed surfaces

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Rupflin, Melanie
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1211.1939
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Citation

Rupflin, M., & Topping, P. M. (2014). A uniform Poincare estimate for quadratic differentials on closed surfaces. Calculus of Variations and Partial Differential Equations, 0759. doi:10.1007/s00526-014-0759-0.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-7C8B-D

Abstract

We prove a uniform estimate, valid for every closed Riemann surface of genus at least two, that bounds the distance of any quadratic differential to the finite dimensional space of holomorphic quadratic differentials in terms of its antiholomorphic derivative.