In the present note, we deal with small perturbations of an infinite cylinder in three-dimensional Euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.
"Minimal disc-type surfaces embedded in a perturbed cylinder." Differential Integral Equations 22 (11/12) 1115 - 1124, November/December 2009. https://doi.org/10.57262/die/1356019407