Constant mean curvature foliation of domains of dependence in 𝐴𝑑𝑆₃ | Zendy

Andrea Tamburelli | Zendy

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Constant mean curvature foliation of domains of dependence in 𝐴𝑑𝑆₃

Author(s) -

Andrea Tamburelli

Publication year - 2017

Publication title -

transactions of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.798

H-Index - 100

eISSN - 1088-6850

pISSN - 0002-9947

DOI - 10.1090/tran/7295

Subject(s) - mathematics , foliation (geology) , constant (computer programming) , mean curvature , geometry , center of curvature , curvature , mathematical analysis , geology , computer science , geochemistry , metamorphic rock , programming language

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

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