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.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://doi.org/10.1016/j.na.2008.10.02400903nas a2200145 4500008004100000245006400041210006300105260002900168300001600197490000700213520043600220100003000656700001900686856005200705 2009 eng d00aMinimal disc-type surfaces embedded in a perturbed cylinder0 aMinimal disctype surfaces embedded in a perturbed cylinder bKhayyam Publishing, Inc. a1115–11240 v223 aIn 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.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://projecteuclid.org/euclid.die/1356019407