7 problems

Bilinear Kakeya range conjecture. $K^*(q'\times q'\to p'/2)$ holds if and only if

Bilinear restriction range conjecture. If $n\geq2$, then $R^*(p\times p\to q)$ holds whenever

Bilinear restriction conjecture. These necessary conditions are sharp: they suffice for the corresponding bilinear restriction estimate. This conjecture is still open except in dim…

Bilinear space-time estimate conjecture. For $2\leq p,r<\infty$, the estimate

Bourgain–Chang bilinear estimate conjecture. For every $\varepsilon>0$, there exists $C_\varepsilon$ such that, for all sufficiently large primes $p$,

Foschi–Klainerman conjecture. For every $(q,r)\in\mathbf{\Gamma}$, there is a constant $C$ depending on $q$, $r$, $\varSigma_1$ and $\varSigma_2$ such that

Let $n\ge 3$, and let $S_1$ and $S_2$ be smooth compact non-empty subsets of the paraboloid in ${\mathbf{R}}\times{\mathbf{R}}^{n-1}$ whose unit normals are separated by at least a…