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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Number of least area planes in Gromov hyperbolic $ 3$-spaces


Author: Baris Coskunuzer
Journal: Proc. Amer. Math. Soc. 138 (2010), 2923-2937
MSC (2010): Primary 53A10, 57M50
Published electronically: April 14, 2010
MathSciNet review: 2644904
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Abstract: We show that for a generic simple closed curve $ \Gamma$ in the asymptotic boundary of a Gromov hyperbolic $ 3$-space with cocompact metric $ X$, there exists a unique least area plane $ \Sigma$ in $ X$ such that $ \partial_{\infty}\Sigma = \Gamma$. This result has interesting topological applications for constructions of canonical $ 2$-dimensional objects in Gromov hyperbolic $ 3$-manifolds.


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Additional Information

Baris Coskunuzer
Affiliation: Department of Mathematics, Koc University, Sariyer, Istanbul 34450, Turkey
Email: bcoskunuzer@ku.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10308-6
PII: S 0002-9939(10)10308-6
Received by editor(s): October 15, 2009
Received by editor(s) in revised form: December 2, 2009
Published electronically: April 14, 2010
Additional Notes: The author is partially supported by EU-FP7 Grant IRG-226062, TUBITAK Grant 107T642 and a TUBA-GEBIP Award
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.