Open AccessA remark on minimal hypercones
Author(s) -
Richard Schoen
Publication year - 1982
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.79.14.4523
Subject(s) - hypersurface , scalar curvature , mathematics , curvature , metric (unit) , pure mathematics , scalar (mathematics) , cone (formal languages) , topology (electrical circuits) , mathematical analysis , combinatorics , geometry , operations management , algorithm , economics
LetM be a minimal hypersurface in the sphere. It is shown that if the cone overM is a stable critical point for the area functional, thenM admits a conformally equivalent metric with positive scalar curvature. This gives both topological and geometric restrictions on such hypersurfacesM .