4 problems

Let $E$ be the extension operator for the truncated parabola, corresponding to $\Gamma(\xi)=\xi^2$, and let $\omega:B_R\to[0,\infty)$ be a one-dimensional weight, so that … for eve…

Parabola decoupling conjecture. For every $1\leq p<6$, there is a constant $C_p$ independent of $\delta$ such that

Let $s\in[1,2)$ and $2\le p\le 2+2s$. Write $D(N,N^s,p)$ for the decoupling constant associated with the parabola at spatial scale $N^s$ and exponent $p$. Uniform decoupling conjec…

Let $\frac12\leq \alpha\leq 1$, and let $\Gamma_\alpha(\delta)$ partition the $\delta$-neighborhood of the truncated parabola … into almost rectangular boxes $\gamma$ of diameter…