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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Properly embedded least area planes in Gromov hyperbolic $ 3$-spaces

Author(s): Baris Coskunuzer
Journal: Proc. Amer. Math. Soc. 136 (2008), 1427-1432.
MSC (2000): Primary 53A10; Secondary 57M50
Posted: December 7, 2007
MathSciNet review: 2367116
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Abstract | References | Similar articles | Additional information

Abstract: Let $ X$ be a Gromov hyperbolic $ 3$-space with cocompact metric, and $ \Si$ the sphere at infinity of $ X$. We show that for any simple closed curve $ \Gamma$ in $ \Si$, there exists a properly embedded least area plane in $ X$ spanning $ \Gamma$. This gives a positive answer to Gabai's conjecture from 1997. Soma has already proven this conjecture in 2004. Our technique here is simpler and more general, and it can be applied to many similar settings.

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Additional Information:

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

DOI: 10.1090/S0002-9939-07-09214-3
PII: S 0002-9939(07)09214-3
Received by editor(s): October 16, 2006
Received by editor(s) in revised form: February 2, 2007
Posted: December 7, 2007
Additional Notes: The author was supported by NSF Grant DMS-0603532
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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