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

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

There is an error for Lemma 3.1. There should be more condition so I think I should withdraw this article and my paper. It is famous problem, so withdrawing is necessary