The Proof of restriction conjecture In ${\mathbb{R}}^3$

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 $p>3$, ${\parallel E_{S}f\parallel }_{L^p\left({\mathbb{R}}^3\right)}\le C(p,S)\mathrm{\parallel }f{\mathrm{\parallel }}_{L^{\mathrm{\infty }}(S)}\mathrm{.}$ The proof of restriction conjecture in ${\mathbb{R}}^3$ implies that Kakeya set conjecture is true when n=3.