A Minimal Lamination with Cantor Set-Like Singularities

2009/10/01 by Stephen J. Kleene, Kleene, Stephen J.
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.0910.0199

15 pages, 3 figures, typos corrected

arxiv created 2011/03/17 · arxiv updated 2011/03/21

Abstract

Given a compact closed subset M of a line segment in ℝ³, we construct a sequence of minimal surfaces Σ_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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