Minimal disc-type surfaces embedded in a perturbed cylinder. (English) Zbl 1240.53004

The paper deals with small preturbations of an infinite cylinder in three-dimensional Euclidian space. Minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly are found. 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.


53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
35R35 Free boundary problems for PDEs