New uniform pointwise bounds for harmonic Beltrami differentials yield optimal lower Weil-Petersson curvature bounds and imply that the average total scalar curvature of moduli space is comparable to -g as genus grows.
Buser, Geometry and spectra of compact Riemann surfaces, Modern Birkh¨ auser Classics
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Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures
New uniform pointwise bounds for harmonic Beltrami differentials yield optimal lower Weil-Petersson curvature bounds and imply that the average total scalar curvature of moduli space is comparable to -g as genus grows.