Constant mean curvature foliation of domains of dependence in 𝐴𝑑𝑆₃

Tamburelli, Andrea

doi:10.1090/tran/7295

Constant mean curvature foliation of domains of dependence in $AdS_{3}$
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Trans. Amer. Math. Soc. 371 (2019), 1359-1378 Request permission

Abstract:

We prove that, given an acausal curve $\Gamma$ in the boundary at infinity of $AdS_{3}$ which is the graph of a quasi-symmetric homeomorphism $\phi$, 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 $\phi$.

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