Inserted: 23 mar 2015
Last Updated: 21 oct 2016
Journal: Comm. Pure Appl. Math.
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.