Fall, Mouhamed Moustapha; Mercuri, Carlo Minimal disc-type surfaces embedded in a perturbed cylinder. (English) Zbl 1240.53004 Differ. Integral Equ. 22, No. 11-12, 1115-1124 (2009). 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. Reviewer: Josef Janyška (Brno) Cited in 3 Documents 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 Keywords:cylinder; minimal disc PDF BibTeX XML Cite \textit{M. M. Fall} and \textit{C. Mercuri}, Differ. Integral Equ. 22, No. 11--12, 1115--1124 (2009; Zbl 1240.53004) OpenURL