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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1982 Jul;79(14):4523–4524. doi: 10.1073/pnas.79.14.4523

A remark on minimal hypercones

Richard Schoen 1
PMCID: PMC346704  PMID: 16593217

Abstract

Let M be a minimal hypersurface in the sphere. It is shown that if the cone over M is a stable critical point for the area functional, then M admits a conformally equivalent metric with positive scalar curvature. This gives both topological and geometric restrictions on such hypersurfaces M.

Keywords: tangent cone, stable hypersurface, scalar curvature

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