Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Positive scalar curvature and minimal hypersurfaces
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C21
  • Retrieve articles in all journals with MSC (2000): 53C21
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