qbiGratulation an Hanna Cairo.
Die 17-jährige Schülerin hat die Vermutung von Mizohata und Takeuchi aus der harmonischen Analysis beantwortet. Sie fand ein Gegenbeispiel.
Paper: https://arxiv.org/abs/2502.06137
A Counterexample to the Mizohata-Takeuchi Conjecture
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.
Prof. Dr. Dennis-Kenji Kipker
medico international
Anne Roth
NFDI
NFDI4DS
DFG