A minimal lamination with Cantor set-like singularities
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- by Stephen J. Kleene PDF
- Proc. Amer. Math. Soc. 140 (2012), 1423-1436 Request permission
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 $M$.References
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Additional Information
- Stephen J. Kleene
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 N. Massachussetts Avenue, Cambridge, Massachusetts 02139
- MR Author ID: 915857
- Email: skleene@math.mit.edu
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1423-1436
- MSC (2010): Primary 53-02
- DOI: https://doi.org/10.1090/S0002-9939-2011-10971-7
- MathSciNet review: 2869127