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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A minimal lamination with Cantor set-like singularities


Author: Stephen J. Kleene
Journal: Proc. Amer. Math. Soc. 140 (2012), 1423-1436
MSC (2010): Primary 53-02
Published electronically: July 28, 2011
MathSciNet review: 2869127
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Abstract: Given a compact closed subset $ M$ of a line segment in $ \mathbb{R}^3$, we construct a sequence of minimal surfaces $ \Sigma_k$ embedded in a neighborhood $ C$ of the line segment that converge smoothly to a limit lamination of $ C$ away from $ M$. Moreover, the curvature of this sequence blows up precisely on $ M$, and the limit lamination has non-removable singularities precisely on the boundary of $ M$.


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Additional Information

Stephen J. Kleene
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 N. Massachussetts Avenue, Cambridge, Massachusetts 02139
Email: skleene@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10971-7
PII: S 0002-9939(2011)10971-7
Received by editor(s): January 15, 2010
Received by editor(s) in revised form: November 5, 2010, and December 23, 2010
Published electronically: July 28, 2011
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.