Quasi-Fuchsian AdS representations are Anosov

Thierry Barbot

Home/Archive/arXiv

arXiv · 0710.0969

Quasi-Fuchsian AdS representations are Anosov

Thierry Barbot

View original source ↗Read source document ↗Export metadata ↓

Abstract

In a recent paper, Q. Mérigot proved that representations in SO(2,n) of uniform lattices of SO(1,n) which are Anosov in the sense of Labourie are quasi-Fuchsian, i.e. are faithfull, discrete, and preserve an acausal subset in the boundary of anti-de Sitter space. In the present paper, we prove the reverse implication. It also includes: -- A construction of Dirichlet domains in the context of anti-de Sitter geometry, -- A proof that spatially compact globally hyperbolic anti-de Sitter spacetimes with acausal limit set admit locally CAT(-1) Cauchy hypersurfaces.

Explore related subjects

math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Thierry Barbot. 2007-10-04. Quasi-Fuchsian AdS representations are Anosov. https://arxiv.org/abs/0710.0969

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A classification result for eternal mean convex flows of finite total curvature type

In this article we partially classify the space of eternal mean convex flows in $\mathbb{R}^3$ of finite total curvature type, a condition implied by finite total curvature. In particular we show that topologically nonplanar ones must flow out of a catenoid in a natural sense.

math.DG↗

arXiv2026

Nonexistence of minimizers for the second conformal eigenvalue near the round sphere in low dimensions

We consider the problem of minimizing the second conformal eigenvalue of the conformal Laplacian in a conformal class of metrics with renormalized volume. We prove, in dimensions $n\in\left\{3,\dotsc,10\right\}$, that a minimizer for this problem does not exist for metrics sufficiently close to the round metric on the sphere. This is in striking contrast with the situation in dimensions $n \ge 11$, where Ammann and Humbert obtained the existence of minimizers for the second conformal eigenvalue on any smooth closed non-locally conformally flat manifold. As a byproduct of our techniques, we also obtain a lower bound on the energy of sign-changing solutions of the \nobreak Yamabe equation in dimensions 3, 4 and 5, which extends a result obtained by Weth in the case of the round sphere.

math.DG↗

arXiv2026

C'est un petit val qui mousse de fonctions

Easy lowering local minima, after introducing valley functions on smooth manifolds gives, without gluing technicities, "M. Morse's lemma's" canonical form, moving critical values and eliminating pair of critical points theorems, reducing the last to its one dimensional case.

math.DG↗