Area-minimizing regions with small volume in Riemannian manifolds with boundary
Mouhamed Moustapha Fall · Pacific Journal of Mathematics · 2009
Given a domain of a Riemannian manifold, we prove that regions minimizing the area (relative to ) are nearly the maxima of the mean curvature of ∂ when their volume tends to zero.We deduce some sharp local relative isoperimetric inequalities involving mean curvature comparisons.