The Proof of restriction conjecture In $\mathbb{R}^{3}$ (2304.01092v2)

Abstract: If S is a smooth compact surface in $\mathbb{R}^{3}$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3$, $\left|E_S f\right|{L^p\left(\mathbb{R}^3\right)} \leq C(p, S)|f|{L^{\infty}(S)}.$ The proof of restriction conjecture in $\mathbb{R}^{3}$ implies that Kakeya set conjecture is true when n=3.