Constant mean curvature foliation of domains of dependence in $AdS_{3}$
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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 $\phi$.References
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Additional Information
- Andrea Tamburelli
- Affiliation: Department of Mathematics, University of Luxembourg, L-4364 Esch-sur-Alzette, Luxembourg
- Address at time of publication: Department of Mathematics, Rice University, Houston, Texas 77005-1982
- Email: andrea_tamburelli@libero.it
- Received by editor(s): March 21, 2017
- Received by editor(s) in revised form: May 29, 2017
- Published electronically: July 20, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 1359-1378
- MSC (2010): Primary 53-XX
- DOI: https://doi.org/10.1090/tran/7295
- MathSciNet review: 3885182