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Positive scalar curvature and minimal hypersurfaces


Author: Harish Seshadri
Journal: Proc. Amer. Math. Soc. 133 (2005), 1497-1504
MSC (2000): Primary 53C21
DOI: https://doi.org/10.1090/S0002-9939-04-07706-8
Published electronically: November 1, 2004
MathSciNet review: 2111951
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Abstract: 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 $s_g \ge \vert T \vert$ or $s_g \ge \vert W \vert$, where $s_g$ is the scalar curvature 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 pertaining to the topology of such hypersurfaces is proved in a special situation.


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Additional Information

Harish Seshadri
Affiliation: Stat-Math Unit, Indian Statistical Institute, Bangalore, India
Address at time of publication: Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Email: harish@isibang.ac.in

DOI: https://doi.org/10.1090/S0002-9939-04-07706-8
Received by editor(s): August 27, 2003
Received by editor(s) in revised form: November 19, 2003, and January 16, 2004
Published electronically: November 1, 2004
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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