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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.11556 |
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| _version_ | 1866913795818913792 |
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| author | Metsch, Alec |
| author_facet | Metsch, Alec |
| contents | We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the squared Riemannian distance. Building upon methods of weak KAM theory, we will establish the existence of $C_{loc}^{1,1}$ optimal pairs for the dual optimal transport problem for probability measures along displacement interpolations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C_{loc}^{1,1}$ optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations Metsch, Alec Optimization and Control We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the squared Riemannian distance. Building upon methods of weak KAM theory, we will establish the existence of $C_{loc}^{1,1}$ optimal pairs for the dual optimal transport problem for probability measures along displacement interpolations. |
| title | $C_{loc}^{1,1}$ optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.11556 |