arXiv:2502.06137math.CA
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.
Linked by 5 identifiable commenters in 5 comments across 3 threads, from Jul 2025 to Aug 2025.
Here's a link to the paper on the arxiv: https://arxiv.org/abs/2502.06137
Heh, take a look at her paper [0]. It is much more complex that TFA makes it out to be: once you have the intuition you need to prove it actually disproves the theorem. Also, it's probably a not very well known conjecture that people wouldn't care too much about. Also also, it…
Paper here: https://arxiv.org/abs/2502.06137 I had the opportunity to take a harmonic analysis course in grad school. I passed it up. It was only tangentially related to my research at the time.
A PhD in the US requires a lot of coursework, aside from research. Perhaps, she is interested in that. Otherwise, some universities, especially in EU, offer PhDs by publication. She could simply wrap up her counter-example publication (https://arxiv.org/pdf/2502.06137) as a…
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Sorry if this is a silly question, but I came across a "white lie" in a paper(https://arxiv.org/html/2502.06137v2#S3.SS2) yesterday: > Throughout this section, we use A≈B to mean that A and B are essentially equal, in the sense that B is a suitable approximation of A in some…
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