We prove that a strictly stable oriented constant-mean-curvature hypersurface in a smooth closed manifold of dimension less than or equal to 7 is uniquely homologically area minimizing for ﬁxed volume in a small _L_1 neighborhood, proving a conjecture of Choksi and Sternberg.
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Antonio Ros, Frank Morgan, Stable constant-mean-curvature hypersurfaces are area minimizing in small <em>L</em><sup>1</sup> neighborhoods. Interfaces Free Bound. 12 (2010), no. 2, pp. 151–155DOI 10.4171/IFB/230