A MINIMAL LAMINATION WITH CANTOR SET-LIKE SINGULARITIES

作者:Kleene Stephen J*
来源:Proceedings of the American Mathematical Society, 2012, 140(4): 1423-1436.

摘要

Given a compact closed subset M of a line segment in 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.

  • 出版日期2012-4