Letting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

%B Nonlinear Analysis: Theory, Methods & Applications %I Elsevier %V 70 %P 4422–4440 %G eng %U https://doi.org/10.1016/j.na.2008.10.024 %R 10.1016/j.na.2008.10.024 %0 Journal Article %J Differential and Integral Equations %D 2009 %T Minimal disc-type surfaces embedded in a perturbed cylinder %A Fall, Mouhamed Moustapha %A Mercuri, Carlo %XIn the present note we deal with small perturbations of an infinite cylinder in the 3D 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.

%B Differential and Integral Equations %I Khayyam Publishing, Inc. %V 22 %P 1115–1124 %G eng %U https://projecteuclid.org/euclid.die/1356019407