Properly embedded least area planes in Gromov hyperbolic -spaces

Author:
Baris Coskunuzer

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1427-1432

MSC (2000):
Primary 53A10; Secondary 57M50

Published electronically:
December 7, 2007

MathSciNet review:
2367116

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Gromov hyperbolic -space with cocompact metric, and the sphere at infinity of . We show that for any simple closed curve in , there exists a properly embedded least area plane in spanning . 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:
http://dx.doi.org/10.1090/S0002-9939-07-09214-3

Received by editor(s):
October 16, 2006

Received by editor(s) in revised form:
February 2, 2007

Published electronically:
December 7, 2007

Additional Notes:
The author was supported by NSF Grant DMS-0603532

Communicated by:
Alexander N. Dranishnikov

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.