A Counterexample to the Mizohata-Takeuchi Conjecture
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915193789874176 |
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| author | Cairo, Hannah |
| author_facet | Cairo, Hannah |
| contents | We derive a family of $L^p$ estimates of the X-Ray transform of positive measures in $\mathbb R^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in $\mathbb R^d$ that does not lie in a hyperplane. In particular, multilinear restriction estimates at the endpoint cannot be sharpened directly by the Mizohata-Takeuchi conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Counterexample to the Mizohata-Takeuchi Conjecture Cairo, Hannah Classical Analysis and ODEs 42B37 We derive a family of $L^p$ estimates of the X-Ray transform of positive measures in $\mathbb R^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in $\mathbb R^d$ that does not lie in a hyperplane. In particular, multilinear restriction estimates at the endpoint cannot be sharpened directly by the Mizohata-Takeuchi conjecture. |
| title | A Counterexample to the Mizohata-Takeuchi Conjecture |
| topic | Classical Analysis and ODEs 42B37 |
| url | https://arxiv.org/abs/2502.06137 |