Positive scalar curvature and minimal hypersurfaces

Details Positive scalar curvature and minimal hypersurfaces Positive scalar curvature and minimal hypersurfaces

2003-08-21

arxiv.org/abs/math/0308203v2

Proc. of AMS, 133 (2005), 1497-1504

Mathematics

Differential Geometry

7 pages

Scientific paper

We show that the minimal hypersurface method of Schoen and Yau can be used for the ``quantitative'' study of positive scalar curvature. More precisely, we show that if a manifold admits a metric $g$ with $s_g \ge | T |$ or $s_g \ge | W |$, where $s_g$ is the scalar curvature of of $g$, $T$ any 2-tensor on $M$ and $W$ the Weyl tensor of $g$, then any closed orientable stable minimal (totally geodesic in the second case) hypersurface also admits a metric with the corresponding positivity of scalar curvature. A corollary about the topology of such hypersurfaces is proved in a special situation.

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