Weak density of smooth maps in \(W^{1, 1}(M,N)\) for non-Abelian \({\pi}_1(N)\) (Q1868400)
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scientific article; zbMATH DE number 1901460
| Language | Label | Description | Also known as |
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| English | Weak density of smooth maps in \(W^{1, 1}(M,N)\) for non-Abelian \({\pi}_1(N)\) |
scientific article; zbMATH DE number 1901460 |
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Weak density of smooth maps in \(W^{1, 1}(M,N)\) for non-Abelian \({\pi}_1(N)\) (English)
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27 April 2003
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Let \(M\) and \(N\) be smooth compact Riemannian manifolds such that \(N\) is closed and isometricly embedded in \({\mathbb R}^N\). Set \[ W^{1,1}(M,N):=\{u\in W^{1,1}(M,{\mathbb R}^N); u(x)\in N \text{ for a.e. } x\in M\}. \] In this paper the author proves that smooth maps are dense in the sense of biting convergence in \(W^{1,1}(M,N)\) (Theorem 1).
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topological singularities
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minimal connections
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density of smooth maps
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Sobolev spaces between manifolds.
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