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On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture

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Hu Z.-J., Wei G.-X.

Colloquium Mathematicum

2003

tom 96

nr 2

213-223

Let M̅ be a compact Riemannian manifold with sectional curvature $K_{M̅}$ satisfying $1/5 < K_{M̅} ≤ 1$ (resp. $2 ≤ K_{M̅} < 10$), 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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Hu Z.-J.

1 Wei G.-X.

1 2003

Wyniki wyszukiwania

On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture