Foliations of small tubes in Riemannian manifolds by capillary minimal discs

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