Homeomorphisms and monotone vector fields (Q2754964)
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scientific article; zbMATH DE number 1668806
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homeomorphisms and monotone vector fields |
scientific article; zbMATH DE number 1668806 |
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5 November 2001
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monotone vector field
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0.8901982
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0.88979197
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0.8863642
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0.8794178
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0.87874454
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Homeomorphisms and monotone vector fields (English)
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A vector field \(X\) on a convex Riemannian manifold is called monotone if the function \(\langle X,\dot\gamma\rangle\) is increasing along all geodesics \(\gamma\). The author shows that on a Hadamard manifold \(M\), the map \(x\mapsto\exp_xX_x\) is an expansive homeomorphism of \(M\). This generalizes a classical result of \textit{G. Minty} for Hilbert spaces in [Duke Math. J. 29, 341-346 (1962; Zbl 0111.31202)].
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