arXiv:1503.06674 Abstract | arXiv Analytics

arXiv:1503.06674 [math.AP]Abstract References Reviews Resources

On the shape of compact hypersurfaces with almost constant mean curvature

Published 2015-03-23, updated 2015-04-10Version 2

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.

Comments: 36 pages, 2 figures. In this version we have added an appendix about almost umbilical surfaces

Categories: math.AP, math.DG, math.MG

Subjects: 49Q10, 49Q20, 53A10

Keywords: constant mean curvature, compact hypersurfaces, scalar mean curvature, disjoint tangent balls, set controls

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