A Minimal Lamination with Cantor Set-Like Singularities

Stephen J. Kleene

A Minimal Lamination with Cantor Set-Like Singularities

Differential Geometry 2011-03-21 v2 Analysis of PDEs

Authors: Stephen J. Kleene

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 $M$ .

Keywords

minimal surfaces minimal hypersurfaces and morse index surfaces and embeddings

Cite

@article{arxiv.0910.0199,
  title  = {A Minimal Lamination with Cantor Set-Like Singularities},
  author = {Stephen J. Kleene},
  journal= {arXiv preprint arXiv:0910.0199},
  year   = {2011}
}

Comments

15 pages, 3 figures, typos corrected

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