A minimal lamination with Cantor set-like singularities

Kleene, Stephen

doi:10.1090/S0002-9939-2011-10971-7

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 $M$.

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