• Corpus ID: 204509256

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}
}
  • Filippo Mazzoli
  • Published 14 October 2019
  • Mathematics
  • arXiv: Differential Geometry
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… 

References

SHOWING 1-10 OF 31 REFERENCES

Notes on the Schwarzian tensor and measured foliations at infinity of quasifuchsian manifolds.

The boundary at infinity of a quasifuchsian hyperbolic manifold is equiped with a holomorphic quadratic differential. Its horizontal measured foliation $f$ can be interpreted as the natural analog of

On the Renormalized Volume of Hyperbolic 3-Manifolds

The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main aim of the present

A Schläfli-type formula for convex cores of hyperbolic 3-manifolds

In 3-dimensional hyperbolic geometry, the classical Schlafli formula expresses the variation of the volume of a hyperbolic polyhedron in terms of the length of its edges and of the variation of its

Un lemme de Morse pour les surfaces convexes

We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the

Asymptotic behavior of Cauchy hypersurfaces in constant curvature space–times

We study the asymptotic behavior of convex Cauchy hypersurfaces on maximal globally hyperbolic spatially compact space–times of constant curvature. We generalise the result of Belraouti (Annales de

The dual Bonahon–Schläfli formula

Given a differentiable deformation of geometrically finite hyperbolic $3$-manifolds $(M_t)_t$, the Bonahon-Schlafli formula expresses the derivative of the volume of the convex cores $(C M_t)_t$ in

Hypersurfaces in Hn and the space of its horospheres

Abstract. A classical theorem, mainly due to Aleksandrov [Al2] and Pogorelov [P], states that any Riemannian metric on S2 with curvature K > —1 is induced on a unique convex surface in H3. A similar

The Schläfli formula in Einstein manifolds with boundary

We give a smooth analogue of the classical Schlafli formula, relating the variation of the volume bounded by a hypersurface moving in a general Einstein manifold and the integral of the variation of

Asymptotically Poincaré surfaces in quasi-Fuchsian manifolds

  • K. Quinn
  • Mathematics
    Proceedings of the American Mathematical Society
  • 2019
We introduce the notion of an asymptotically Poincar\'e family of surfaces in an end of a quasi-Fuchsian manifold. We show that any such family gives a foliation of an end by asymptotically parallel

Hyperbolic manifolds with convex boundary

Let (M,∂M) be a 3-manifold, which carries a hyperbolic metric with convex boundary. We consider the hyperbolic metrics on M such that the boundary is smooth and strictly convex. We show that the