Embedded plateau problem

Author:
Baris Coskunuzer

Journal:
Trans. Amer. Math. Soc. **364** (2012), 1211-1224

MSC (2010):
Primary 53A10; Secondary 57M50, 49Q05

DOI:
https://doi.org/10.1090/S0002-9947-2011-05486-3

Published electronically:
October 19, 2011

MathSciNet review:
2869175

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if is a simple closed curve bounding an embedded disk in a closed -manifold , then there exists a disk in with boundary such that minimizes the area among the embedded disks with boundary . Moreover, is smooth, minimal and embedded everywhere except where the boundary meets the interior of . 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:
https://doi.org/10.1090/S0002-9947-2011-05486-3

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.