Regularity of minimizing harmonic maps into \(S^ 4\), \(S^ 5\) and symmetric spaces (Q1318130)
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scientific article; zbMATH DE number 537316
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularity of minimizing harmonic maps into \(S^ 4\), \(S^ 5\) and symmetric spaces |
scientific article; zbMATH DE number 537316 |
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Regularity of minimizing harmonic maps into \(S^ 4\), \(S^ 5\) and symmetric spaces (English)
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31 May 1994
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We prove that for \(n=4\), 5 every energy minimizing map from a manifold \(M\) of dimension \(n\) into the Euclidean sphere \(S^ n\) is regular in the interior of \(M\). This improves a result of R. Schoen and K. Uhlenbeck. We also prove a Liouville type theorem for smooth stable harmonic maps from noncompact complete Riemannian manifolds with nonnegative Ricci curvature into \(S^ n\).
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minimizing harmonic maps
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regularity
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Kato's inequality
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stability
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