Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume

Martin Bridgeman, Jeffrey Brock, Kenneth Bromberg

To a complex projective structure $\Sigma$ on a surface, Thurston associates a locally convex pleated surface. We derive bounds on the geometry of both in terms of the norms $\|ϕ_Σ\|_\i…