Constant mean curvature foliation of domains of dependence in $AdS_{3}$

Andrea Tamburelli

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arXiv · 1610.08867

Constant mean curvature foliation of domains of dependence in $AdS_{3}$

Andrea Tamburelli

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Abstract

We prove that, given an acausal curve $Γ$ in the boundary at infinity of $AdS_{3}$ which is the graph of a quasi-symmetric homeomorphism $ϕ$, there exists a unique foliation of its domain of dependence $D(Γ)$ by constant mean curvature surfaces with bounded second fundamental form. Moreover, these surfaces provide a family of quasi-conformal extensions of $ϕ$.

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Andrea Tamburelli. 2017-03-21. Constant mean curvature foliation of domains of dependence in $AdS_{3}$. https://arxiv.org/abs/1610.08867

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