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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On stable currents and positively curved hypersurfaces


Authors: Yi-Bing Shen and Qun He
Journal: Proc. Amer. Math. Soc. 129 (2001), 237-246
MSC (1991): Primary 53C42; Secondary 58A25
Published electronically: June 7, 2000
MathSciNet review: 1784025
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Abstract:

We establish a nonexistence theorem for stable currents (or stable varifolds) in complete $\delta$-pinched hypersurfaces of a real space form with nonnegative constant sectional curvature. This is a partial positive answer to the well-known conjecture of Lawson and Simons.


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Additional Information

Yi-Bing Shen
Affiliation: Department of Mathematics, West-Brook Campus, Zhejiang University, Hangzhou 310028, People’s Republic of China
Email: ybshen@dial.zju.edu.cn

Qun He
Affiliation: Department of Mathematics, West-Brook Campus, Zhejiang University, Hangzhou 310028, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05753-1
PII: S 0002-9939(00)05753-1
Keywords: Stable currents, $\delta $-pinched manifolds, $\delta $-pinched hypersurfaces
Received by editor(s): March 15, 1999
Published electronically: June 7, 2000
Additional Notes: This research was supported in part by NNSFC and NSFZP
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2000 American Mathematical Society