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

@article{Bridgeman2017SchwarzianDP,
  title={Schwarzian derivatives, projective structures, and the Weil–Petersson gradient flow for renormalized volume},
  author={Martin J. Bridgeman and Jeffrey Brock and Kenneth W. Bromberg},
  journal={Duke Mathematical Journal},
  year={2017},
  volume={168},
  pages={867-896}
}
  • Martin J. Bridgeman, Jeffrey Brock, Kenneth W. Bromberg
  • Published 2017
  • Mathematics
  • Duke Mathematical Journal
  • 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 $\|\phi_\Sigma\|_\infty$ and $\|\phi_\Sigma\|_2$ of the quadratic differential $\phi_\Sigma$ of $\Sigma$ given by the Schwarzian derivative of the associated locally univalent map. We show that these give a unifying approach that generalizes a number of important, well known results for convex cocompact hyperbolic… CONTINUE READING