Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A minimal lamination with Cantor set-like singularities
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53-02
  • Retrieve articles in all journals with MSC (2010): 53-02
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