Minimal Smoothings of Area Minimizing Cones
Abstract
In this paper we show that every area minimizing cone C^{n1} in R^n can be approximated by entirely smooth area minimizing hypersurfaces. This extensively uses hyperbolic unfoldings of such hypersurfaces and the resulting potential theory for the Jacobi field operator. Applications include the splitting theorem in scalar curvature geometry saying that any (n1)dim. homology class of a compact manifold M^n with positive scalar curvature can be represented by a smooth (!) compact hypersurface that admits a positive scalar curvature metric.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.03157
 arXiv:
 arXiv:1810.03157
 Bibcode:
 2018arXiv181003157L
 Keywords:

 Mathematics  Differential Geometry