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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Embedded plateau problem


Author: Baris Coskunuzer
Journal: Trans. Amer. Math. Soc. 364 (2012), 1211-1224
MSC (2010): Primary 53A10; Secondary 57M50, 49Q05
Published electronically: October 19, 2011
MathSciNet review: 2869175
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Abstract: We show that if $ \Gamma $ is a simple closed curve bounding an embedded disk in a closed $ 3$-manifold $ M$, then there exists a disk $ \Sigma $ in $ M$ with boundary $ \Gamma $ such that $ \Sigma $ minimizes the area among the embedded disks with boundary $ \Gamma $. Moreover, $ \Sigma $ is smooth, minimal and embedded everywhere except where the boundary $ \Gamma $ meets the interior of $ \Sigma $. The same result is also valid for homogeneously regular manifolds with sufficiently convex boundary.


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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/S0002-9947-2011-05486-3
PII: S 0002-9947(2011)05486-3
Received by editor(s): April 28, 2009
Received by editor(s) in revised form: February 25, 2010
Published electronically: October 19, 2011
Additional Notes: The author was partially supported by EU-FP7 Grant IRG-226062 and TUBITAK Grant 109T685
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.