On the nonexistence of stable minimal submanifolds in positively pinched Riemannian manifolds (Q2735680)
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scientific article; zbMATH DE number 1641154
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nonexistence of stable minimal submanifolds in positively pinched Riemannian manifolds |
scientific article; zbMATH DE number 1641154 |
Statements
13 December 2001
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\(\delta\)-pinched Riemannian manifold
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stable minimal submanifold
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On the nonexistence of stable minimal submanifolds in positively pinched Riemannian manifolds (English)
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\textit{H. B. Lawson} and \textit{J. Simons} [Ann. Math. (2) 98, 427-450 (1973; Zbl 0283.53049)] conjectured that there are no compact stable minimal submanifolds in a compact simply connected \(1/4\)-pinched Riemannian manifold. The authors prove the following result which supports the conjecture of Lawson and Simons: There are no compact stable minimal submanifolds in a compact simply connected \(0.77\)-pinched Riemannian manifold.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].
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