Spectral Obstructions to Contracting Transport Maps on Curved Spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916042343710720 |
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| author | Aryan, Shrey |
| author_facet | Aryan, Shrey |
| contents | Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is 1-Lipschitz. Owing to its many applications in analysis, probability, and geometry, the problem of extending this theorem to curved spaces has appeared repeatedly in the literature, going back to Villani [V09]. More recently, Milman [Mil18] formulated precise conjectures in this direction. In this work, we construct counterexamples to these conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24705 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Obstructions to Contracting Transport Maps on Curved Spaces Aryan, Shrey Differential Geometry Probability Spectral Theory 53C21 (primary), 58J50, 35P15, 53C20 Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is 1-Lipschitz. Owing to its many applications in analysis, probability, and geometry, the problem of extending this theorem to curved spaces has appeared repeatedly in the literature, going back to Villani [V09]. More recently, Milman [Mil18] formulated precise conjectures in this direction. In this work, we construct counterexamples to these conjectures. |
| title | Spectral Obstructions to Contracting Transport Maps on Curved Spaces |
| topic | Differential Geometry Probability Spectral Theory 53C21 (primary), 58J50, 35P15, 53C20 |
| url | https://arxiv.org/abs/2605.24705 |