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.

PB - Elsevier VL - 70 UR - https://doi.org/10.1016/j.na.2008.10.024 ER - TY - JOUR T1 - Minimal disc-type surfaces embedded in a perturbed cylinder JF - Differential and Integral Equations Y1 - 2009 A1 - Fall, Mouhamed Moustapha A1 - Mercuri, Carlo AB -In 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.

PB - Khayyam Publishing, Inc. VL - 22 UR - https://projecteuclid.org/euclid.die/1356019407 ER -