Calculus of Variations and Geometric Measure Theory

L. Ruffoni - F. Tripaldi

Extending an example by Colding and Minicozzi

created by tripaldi on 03 Jun 2020


Published Paper

Inserted: 3 jun 2020
Last Updated: 3 jun 2020

Journal: The Journal of Geometric Analysis
Volume: 30
Pages: 1028–1041
Year: 2019

ArXiv: 1810.00359 PDF


Extending an example by Colding and Minicozzi, we construct a sequence of properly embedded minimal disks $\Sigma_i$ in an infinite Euclidean cylinder around the $x_3$-axis with curvature blow-up at a single point. The sequence converges to a non smooth and non proper minimal lamination in the cylinder. Moreover, we show that the disks $\Sigma_i$ are not properly embedded in a sequence of open subsets of $\mathbb{ R}^3$ that exhausts $\mathbb{ R}^3$.