Estimates for the norm of the second fundamental form, ∣A∣, play a crucial
role in studying the geometry of surfaces. In fact, when ∣A∣ is bounded the
surface cannot bend too sharply. In this paper we prove that for an embedded
geodesic disk with bounded L2 norm of ∣A∣, ∣A∣ is bounded at interior
points, provided that the W1,p norm of its mean curvature is sufficiently
small, p>2. In doing this we generalize some renowned estimates on ∣A∣ for
minimal surfaces.Comment: 17 pages, no figures, submitte