On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture
Ze-Jun Hu ; Guo-Xin Wei
Colloquium Mathematicae, Tome 96 (2003), p. 213-223 / Harvested from The Polish Digital Mathematics Library
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Let M̅ be a compact Riemannian manifold with sectional curvature KM̅ satisfying 1/5<KM̅≤1 (resp. 2≤KM̅<10), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:284869 
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Ze-Jun Hu; Guo-Xin Wei. On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture. Colloquium Mathematicae, Tome 96 (2003) pp. 213-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-2-6/