7 problems

Cone restriction conjecture. The estimate

Bennett--Jeavons--Olver--Soffer conjecture. The function $f_\star^{(s)}$ is a maximizer of

Spherical exponential maximizer conjecture. For all $f$,

Foschi's conjecture. The function $f(\tau,\xi)=e^{-|\tau|}$ should maximize

The $k$-restriction conjecture for the cone. One expects

Let ${{\mathbb C}}o^2=\\{(\xi_1,\xi_2,\sqrt{\xi_1^2+\xi_2^2}):1\leq \xi_1^2+\xi_2^2\leq 2\\}$ be the truncated cone, and let $\Gamma(\delta)$ partition its $\delta$-neighborhood in…

Let ${\mathcal C}^2=\{(\xi_1,\xi_2,\sqrt{\xi_1^2+\xi_2^2}):\frac14\leq\xi_1^2+\xi_2^2\leq4\}$, and let ${\mathcal N}_\delta({\mathcal C}^2)$ denote its $\delta$-neighborhood. Suppo…