Nonexistence theorems for \(p\)-harmonic maps (Q2720059)
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scientific article; zbMATH DE number 1610548
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonexistence theorems for \(p\)-harmonic maps |
scientific article; zbMATH DE number 1610548 |
Statements
17 October 2002
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p-harmonic map
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p-stress-energy tensor
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Hessian comparison theorem
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Nonexistence theorems for \(p\)-harmonic maps (English)
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The \(p\)-stress-energy tensor for certain smooth maps between Riemannian manifolds is defined and its basic properties are studied. Making use of its properties and the Hessian comparison theorem the author proves: Let \(M\) be a simply-connected complete Riemannian manifold of \(\dim M\geq 2\) of non-positive sectional curvature. Then there does not exist a non-constant \(p\)-harmonic map with slowly divergent \(p\)-energy.
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