×

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.

MSC:

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
PDF BibTeX XML Cite