Search results for "laminations"
showing 2 items of 2 documents
Laminations and tilings of the Hyperbolic upper half plane
2005
This thesis is devoted to the study of dynamical systems associated with tilings of theEuclidean plane or of the Hyperbolic half-plane. A such tiling codes an action of a group ofisometries (namely the group of translations of the plane or the group of affine maps) on a compactmetric space $\Omega$ such that the properties of this action are related with the combinatoricproperties of the tiling. The behaviors of the actions obtained by this way are really various. Insome cases, like for example for the Penrose's tiling, this action is free and minimal. This givesto the set $\Omega$ a structure of a specific lamination called {\it solenoid}. This space islocally the product of a Cantor set w…
Extending an example by Colding and Minicozzi
2018
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 $\mathbb{ R}^3$.