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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Author: Andrea Tamburelli
Journal: Trans. Amer. Math. Soc. 371 (2019), 1359-1378
MSC (2010): Primary 53-XX
DOI: https://doi.org/10.1090/tran/7295
Published electronically: July 20, 2018
MathSciNet review: 3885182
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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 $.


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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

DOI: https://doi.org/10.1090/tran/7295
Received by editor(s): March 21, 2017
Received by editor(s) in revised form: May 29, 2017
Published electronically: July 20, 2018
Article copyright: © Copyright 2018 American Mathematical Society