Small Two Spheres in Positive Scalar Curvature, Using Minimal Hypersurfaces
Abstract
In this survey, we review some results on the area of topologically non-trivial two spheres in manifolds with positive scalar curvature of dimension at most 7. The main tool to get those results is the use of stable minimal hypersurfaces, and we give a short exposition of the usual ways to take advantage of these in the presence of positive scalar: second variation, conformal method, Fischer-Colbrie–Schoen symmetrization, and µ-bubbles. The last section lists some open problems in the area.
Domains
Differential Geometry [math.DG]Origin | Files produced by the author(s) |
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