Constant mean curvature foliation of domains of dependence in $Ad{S}_3$

Abstract

We prove that, given an acausal curve $\Gamma$ in the boundary at infinity of $Ad{S}_3$ which is the graph of a quasi-symmetric homeomorphism $\varphi$, there exists a unique foliation of its domain of dependence $D(\Gamma )$ by constant mean curvature surfaces with bounded second fundamental form. Moreover, these surfaces provide a family of quasi-conformal extensions of $\varphi$.

v.3 Typos corrected and exposition improved. 22 pages

References in corpus (1)

• Some open questions on anti-de Sitter geometry

Cited by in corpus (1)

• Constant mean curvature foliation of globally hyperbolic (2+1)-spacetimes with particles