Number of least area planes in Gromov hyperbolic $3$-spaces
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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.References
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Additional Information
- Baris Coskunuzer
- Affiliation: Department of Mathematics, Koc University, Sariyer, Istanbul 34450, Turkey
- Email: bcoskunuzer@ku.edu.tr
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2923-2937
- MSC (2010): Primary 53A10, 57M50
- DOI: https://doi.org/10.1090/S0002-9939-10-10308-6
- MathSciNet review: 2644904