Foliations of small tubes in Riemannian manifolds by capillary minimal discs

Abstract

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