Number of least area planes in Gromov hyperbolic -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 | References | Similar Articles | Additional Information

Abstract: We show that for a generic simple closed curve in the asymptotic boundary of a Gromov hyperbolic -space with cocompact metric , there exists a unique least area plane in such that . This result has interesting topological applications for constructions of canonical -dimensional objects in Gromov hyperbolic -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

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.