JournalsifbVol. 12, No. 2pp. 151–155

Stable constant-mean-curvature hypersurfaces are area minimizing in small <em>L</em><sup>1</sup> neighborhoods

  • Antonio Ros

    Universidad de Granada, Spain
  • Frank Morgan

    Williams College, Williamstown, USA
Stable constant-mean-curvature hypersurfaces are area minimizing in small <em>L</em><sup>1</sup> neighborhoods cover
Download PDF

Abstract

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.

Cite this article

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. 151–155

DOI 10.4171/IFB/230