# Constant Gaussian curvature foliations and Schläfli formulas of hyperbolic 3-manifolds

@article{Mazzoli2019ConstantGC, title={Constant Gaussian curvature foliations and Schl{\"a}fli formulas of hyperbolic 3-manifolds}, author={Filippo Mazzoli}, journal={arXiv: Differential Geometry}, year={2019} }

We study the geometry of the foliation by constant Gaussian curvature surfaces $(\Sigma_k)_k$ of a hyperbolic end, and how it relates to the structures of its boundary at infinity and of its pleated boundary. First, we show that the Thurston and the Schwarzian parametrizations are the limits of two families of parametrizations of the space of hyperbolic ends, defined by Labourie in 1992 in terms of the geometry of the leaves $\Sigma_k$. We give a new description of the renormalized volume using…

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