*Published Paper*

**Inserted:** 21 dec 2019

**Last Updated:** 3 jan 2020

**Journal:** The Journal of Geometric Analysis

**Year:** 2019

**Doi:** 10.1007/s12220-019-00177-4

**Abstract:**

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 $\mathbb{ R}^3$.