• Corpus ID: 211677606

The Weil-Petersson gradient flow of renormalized volume and 3-dimensional convex cores

  title={The Weil-Petersson gradient flow of renormalized volume and 3-dimensional convex cores},
  author={Martin Bridgeman and Jeffrey F. Brock and Ken Bromberg},
  journal={arXiv: Geometric Topology},
In this paper, we use the Weil-Petersson gradient flow for renormalized volume to study the space $CC(N;S,X)$ of convex cocompact hyperbolic structures on the relatively acylindrical 3-manifold $(N;S)$. Among the cases of interest are the deformation space of an acylindrical manifold and the Bers slice of quasi-Fuchsian space associated to a fixed surface. To treat the possibility of degeneration along flow-lines to peripherally cusped structures, we introduce a surgery procedure to yield a… 
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