5 problems

Positive boundedness conjecture. Every such datum $\mathbf{H}_\mathbf{M}$ is $\mathbf{p}$-bounded.

For each $1\leq j\leq m$, let $\Sigma_j:U_j\to\mathbb{R}^n$ be a smooth parametrization of an $n_j$-dimensional submanifold $S_j$ by a neighborhood $U_j$ of the origin in…

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…

Let $f$ be an even probability density on $\mathbb{R}$ with variance $1$, and let … be the standard normal density. Let $\mu$ be an even isotropic measure on $S^{n-1}$ supported at…

Multilinear restriction conjecture. Under these assumptions, there is a constant $C$, depending on finitely many derivatives of the $\Sigma_i$, the sets $U_i$, $\nu$, and $n$, such…