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Multi-valued graphs in embedded constant mean curvature disks


Author: Giuseppe Tinaglia
Journal: Trans. Amer. Math. Soc. 359 (2007), 143-164
MSC (2000): Primary 53A10
DOI: https://doi.org/10.1090/S0002-9947-06-04095-5
Published electronically: August 24, 2006
MathSciNet review: 2247886
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Abstract: In this paper we prove that an embedded constant mean curvature disk with Gaussian curvature large at a point contains a multi-valued graph around that point on the scale of $ \vert A\vert^2$. This generalizes Colding and Minicozzi's result for minimal surfaces.


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Additional Information

Giuseppe Tinaglia
Affiliation: Department of Mathematics, Johns Hopkins University, 3400 North Charles Street, 404 Krieger Hall, Baltimore, Maryland 21218-2686
Address at time of publication: Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, Indiana 46556-4618
Email: tinaglia@math.jhu.edu, giuseppetinaglia@nd.edu

DOI: https://doi.org/10.1090/S0002-9947-06-04095-5
Received by editor(s): October 4, 2004
Published electronically: August 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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