The Monge--Kantorovich problem, the Schur--Horn theorem, and the diffeomorphism group of the annulus
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917988630790144 |
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| author | Bloch, Anthony M. Ratiu, Tudor S. |
| author_facet | Bloch, Anthony M. Ratiu, Tudor S. |
| contents | First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the annulus. In both cases, we show how the problem can be linked to permutohedra, majorization, and to gradient flows with respect to a suitable metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Monge--Kantorovich problem, the Schur--Horn theorem, and the diffeomorphism group of the annulus Bloch, Anthony M. Ratiu, Tudor S. Optimization and Control 49 First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the annulus. In both cases, we show how the problem can be linked to permutohedra, majorization, and to gradient flows with respect to a suitable metric. |
| title | The Monge--Kantorovich problem, the Schur--Horn theorem, and the diffeomorphism group of the annulus |
| topic | Optimization and Control 49 |
| url | https://arxiv.org/abs/2504.12924 |