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Positive scalar curvature and minimal hypersurfaces

Seshadri, Harish (2005) Positive scalar curvature and minimal hypersurfaces. In: Proceedings Of The American Mathematical Society, 133 (5). pp. 1497-1504.

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Official URL: http://www.ams.org/proc/2005-133-05/S0002-9939-04-...

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) greater than or equal to | T| or s(g) greater than or equal to | W|, 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.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Amer Mathematical Soc.
Keywords: Manifolds
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 04 Feb 2010 07:43
Last Modified: 04 Feb 2010 07:43
URI: http://eprints.iisc.ernet.in/id/eprint/17284

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