Positive scalar curvature and minimal hypersurfaces
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- by Harish Seshadri PDF
- Proc. Amer. Math. Soc. 133 (2005), 1497-1504 Request permission
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.References
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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
- MR Author ID: 712201
- Email: harish@isibang.ac.in
- 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
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1497-1504
- MSC (2000): Primary 53C21
- DOI: https://doi.org/10.1090/S0002-9939-04-07706-8
- MathSciNet review: 2111951