5 problems

Let $U_1,U_2,U_3\subset\mathbb{R}^2$ be caps for the two-dimensional paraboloid satisfying the stated transversality hypothesis, and let $\mathcal{E}_{U_j}$ be the corresponding ex…

Let $k\geq2$, and let $U_1,\ldots,U_k$ parametrize transversal caps of the paraboloid $x\mapsto|x|^2$ in $\mathbb{R}^{d+1}$. For functions $g_j$ on $U_j$, write $p'$ for the Hölder…

Let $2\leq k\leq d+1$, let $U_j\subset\mathbb{R}^d$ be compact connected domains, and let … Assume that the caps parametrized by $U_j$ are transversal. The multilinear extension co…

Let $V$ be a manifold and let $\Gamma_1,\dots,\Gamma_n$ be a transverse family of good fibrations of $V$, with corresponding maps $\pi_j:V\to U_j$ and forms $\omega_j$. For each…

$k$-linear restriction conjecture. The estimate