3 problems

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 $V$ 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…

Endpoint multilinear $k_j$-restriction conjecture. When the $U_j$ are sufficiently small,